Derivatives Definition and 1000 Threads

In finance, a derivative is a contract that derives its value from the performance of an underlying entity. This underlying entity can be an asset, index, or interest rate, and is often simply called the "underlying". Derivatives can be used for a number of purposes, including insuring against price movements (hedging), increasing exposure to price movements for speculation, or getting access to otherwise hard-to-trade assets or markets.
Some of the more common derivatives include forwards, futures, options, swaps, and variations of these such as synthetic collateralized debt obligations and credit default swaps. Most derivatives are traded over-the-counter (off-exchange) or on an exchange such as the Chicago Mercantile Exchange, while most insurance contracts have developed into a separate industry. In the United States, after the financial crisis of 2007–2009, there has been increased pressure to move derivatives to trade on exchanges.
Derivatives are one of the three main categories of financial instruments, the other two being equity (i.e., stocks or shares) and debt (i.e., bonds and mortgages). The oldest example of a derivative in history, attested to by Aristotle, is thought to be a contract transaction of olives, entered into by ancient Greek philosopher Thales, who made a profit in the exchange. Bucket shops, outlawed in 1936, are a more recent historical example.

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  1. M

    Higher order partial derivatives

    Consider the partial di erential equation, (y4-x2)uxx - 2xyuxy - y2uyy = 1. We will make the substitution x = s2 - t2 and y = s - t, to simplify (a) Solve for s and t as functions of x and y the farthest point i got to was x = s^2 - t^2 = (s+t)(s-t) = y(s+t) y = s - t s+t = x/y i...
  2. R

    3rd order derivatives in the lagrangian

    I heard that in classical field theory, terms in the Lagrangian cannot have more than two derivatives acting on them. Why is this? In quantum field theory, I read somewhere that having more than two derivatives on a term in the Lagrangian leads to a violation of Poincare invariance. Is this...
  3. r-soy

    Solving for Tangent Lines and Range of Slopes for a Given Curve

    Hi all I hve two Q I want the explaine how to solve Q1 :(A) Find an equation for tangent to curve y = X^3 - 4X + 1 at the point (2,1) (b ) What is the range of values of the curve's slope Number ( A ) I can solve it but ( B) I face problem to solve...
  4. r-soy

    X^0 - 3Find Older Derivatives of y

    Q Find all older derivatives y = X^4/2 = 3/2X^2 -X y4 = 2X^2 - 3 x ^ 1 - 0 y4 = 4X^1 - 3 -0 y4 = 7
  5. S

    Partial Derivatives - Finding tangent in a volume?

    Not sure I understand exactly what this question is asking. This is obviously a volume in R3 and so how do you get a tangent inside a volume? Or is it just along the plane y = 2 intersecting the volume? Also, what is a parametric equation...? Thanks for the help: Question: The ellipsoid 4x^2...
  6. Battlemage!

    Can Quotient Rule Be Applied to Partial Derivatives?

    My question revolves around the following derivative: for z(x,y) *sorry I can't seem to get the latex right. ∂/∂x (∂z/∂y) What I thought about doing was using the quotient rule to see what I would get (as if these were regular differentials). So, I "factored out" the 1/∂x, then did...
  7. A

    Perturbation theory and total derivatives

    Hi I was just reading about that total derivatives in the Lagrangian does not give any contributions in perturbation theory but that they can play role in non perturbative regimes. But there was no statement WHY that is so? Does anyone have an idea and reading advices? I have the most...
  8. C

    Partial derivatives and chain rule

    Homework Statement express (\frac{\partial u}{\partial s})_{v} in terms of partial derivatives of u(s,t) and t(s,v) Homework Equations The Attempt at a Solution I'm pretty stuck with this problem. I know that dv = (\frac{\partial v}{\partial s})_{t} ds + (\frac{\partial...
  9. C

    Solving f(x) = 5e^(2x+1) with Chain Rule

    Homework Statement f(x) = 5e^(2x+1) Homework Equations Chain rule, power rule and constant multiplies rule The Attempt at a Solution f(x) = 5e^(2x+1) = 5f(x) e^(2x+1) f(u) = e^x f'(u) = e^x g(x)= 2x+1 g'(x) = 2 5f'(x) = 2e^2x+1 =10e^2x+1 Is that...
  10. S

    Are the following two derivatives same?

    1. fxy 2. fyx Are the above 2 derivatives equal, in general. Please explain if you know the answer. Regards, -sgsawant
  11. L

    Interchanging partial derivatives and integrals

    In the midst of https://www.physicsforums.com/showthread.php?t=403002", I came upon a rather interesting, though probably elementary, question. Analagous to the fundamental theorem of calculus, is there a formula or theorem concerning the expression \frac{\partial}{\partial...
  12. S

    Velocity/acceleration using derivatives (answer check)

    Homework Statement An object is traveling along a linear path according to the equation s(t) = 4t^3 - 3t^2 + 5 where t is measured in seconds and s(t) measured in meters. 1. How fast is the object moving at t = 4 seconds? 2. What is the position of the object when it stops...
  13. T

    Help with simplifying derivatives when sketching graphs

    Homework Statement Sketch the graph of x ^ (4/9) * e ^ (-x) Homework Equations None. The Attempt at a Solution My y' = -x ^ (4/9) * e ^ (-x) ( 1 - 4/9x ^ 1/9). I keep on getting a reaaally long derivative for y'' and thus cannot place it on my sign table. Could someone please...
  14. R

    Slope of the tangent line of an intersection - Directional Derivatives

    Homework Statement Find the slope of the tangent line to the curve of intersection of the vertical plane x - y + 1 =0 and the surface z = x2+y2 at the point (1, 2, 5) Homework Equations Gradients, Cross products The Attempt at a Solution I'm pretty lost here. I think I have to...
  15. P

    Derivatives and fractions (relationship?)

    learning calculus here. got differential calculus, though it is a little foggy, and most of integral calculus, which is a little foggier. also using very unpolished precalc background, though i did give most of it a once-over. i have many questions which i can't think of, but of the top of my...
  16. mnb96

    Discrete derivatives with finite-differences

    Hello, I have a function in discrete domain f:\mathbb{Z}\rightarrow \mathbb{R}, and I assume that f is an approximation of another differentiable function g:\mathbb{R}\rightarrow \mathbb{R}. In other words f(n)=g(n), n\in \mathbb{Z}. When one wants to approximate the first derivative of g...
  17. M

    Derivatives & Limits: Solving "Does Not Exist

    Homework Statement lim (e^(7x)-1)/x^2 x-->0 The Attempt at a Solution I typed in "does not exist" and it was wrong.
  18. D

    Derivatives / partial derivatives rule

    When I am taking a partial derivative of an equation with respect to theta_dot, then theta is constant, right? What if I am taking partial derivative with respect to theta, will theta_dot be constant? In this case, theta_dot = omega (angular velocity), but I must keep equation in terms of...
  19. L

    Are First and Second Derivative Calculations for |x-a| - |x+a| Correct?

    Hey I have been asked to find the first and second derivatives of lx-al-lx+al I have, for the first derivative got, sign(x-a)-sign(x+a) and for the second, i have: 2(delta)(x-a)-2(delta)(x+a) am i right in both cases? I also have to draw them 'schematically' how do i do this?
  20. V

    Just a quick question about partial derivatives

    Not a homework question, but It will help me none the less, In my book it says \frac{d}{dt} \int_{-\infty}^{\infty} |\Psi(x,t)|^2 dx is equivalent to \int_{-\infty}^{\infty} \frac{\partial}{\partial t}|\Psi(x,t)|^2 dx I understand how It becomes a partial derivative, since I'm...
  21. R

    Partial derivatives as basis vectors?

    Hi, I'm having trouble understanding how people can make calculations using the partial derivatives as basis vectors on a manifold. Are you allowed to specify a scalar field on which they can operate? eg. in GR, can you define f(x,y,z,t) = x + y + z + t, in order to recover the Cartesian...
  22. S

    How Do You Calculate Derivatives of Composite Functions?

    Homework Statement a) (f ° g)′(−2) = ? b) (g ° f)′(2) = ? Homework Equations f(−2) = −3, g(−2) = −4, f(2) = 3, g(2) = −3, f ′(−2) = −1, f ′(−4) = −2, f ′(2) = 5, g ′(−2) = 1, g ′(2) = 2, g ′(3) = −4. The Attempt at a Solution I have no idea how to do it every thing I've tried...
  23. L

    Partial Derivatives: Show bz(x)=az(y)

    Homework Statement Suppose that z=f(ax+by), where a and b are constants. Show that bz(x) = az(y). z(x) means partial derivative of z with respect to x, as for z(y). Homework Equations The Attempt at a Solution Say z=ax+by z(x) = a z(y) = b So bz(x) = ba = ab = az(y)...
  24. R

    Why is the result not always 0 in the product rule for derivatives?

    [x_{\alpha}, p_{\alpha}]\psi(r)=[x_{\alpha}(-i\hbar \frac{\partial}{{ \partial x_\alpha}})-(-i\hbar\frac{\partial}{\partial x_{\alpha}})x_{\alpha}]\psi(r) why the result is i\hbar\psi(r) should not be 0? and then the same situation why in this case we get 0? [x_{\beta}...
  25. I

    Total differential for finding higer row derivatives

    Homework Statement Well, let's take F: x^2 y^3=0 . Now, let's say thay y=y(x), y being an implicit function of x. I want to find 2nd row derivative \frac{d^2y}{dx^2} using differential operator. Homework Equations not apply The Attempt at a Solution Using D for the first...
  26. T

    Derivatives of trigonometric functions

    Homework Statement Find the constants A and B such that the function y = Asinx + Bcosx satisfies the differential equation y'' + y' - 2y = sinx Homework Equations None The Attempt at a Solution My attempt: y = Asin x + Bcosx y' = Acosx - Bsinx y'' = - Asin x - Bcosx y''...
  27. C

    Calc - Derivatives and Differentiation of Logs

    Homework Statement I have a few problems that are giving me some trouble: 1. Take the derivative of xe-4x 2. Find dy/dx and evaluate the slope for the curve ey^3 - 2x4 + y2 = 3 at (8,0) 3. Find dy/dx and evaluate the slope for the curve e-y - 4 = x2 + 1 at (-2,2) Homework Equations N/A...
  28. D

    Calc derivatives - Minimum total surface area in a box of V = 160 ft2

    Hi everyone! I'm new to online math forums. I wonder if anyone can give me a hand on this - it would be greatly appreciated. Thank you in advance! Dave Homework Statement If a box with a square base and an open top is to have a volume of 160 cubic feet, find the dimensions of the box having...
  29. V

    Derivatives: Taking it in a Circle

    Hello, How is Taking the derivative on the top and bottom makes it go in circles Thank you
  30. S

    Partial Derivatives: Proving & Evaluating at (0,0)

    Do I need to use Schwarz's or Young's theorems to prove it, if don't then do I need to evaluate them on (0,0) using definition.
  31. S

    How Can I Solve a Question on Directional Derivatives Without Knowing the Point?

    According to the statement(attached file) in order to find the directional derivative I must know unit vector along the direction and the point at which to find the directional derivatives. From the angle I can find out the direction (as the cosine of the angle) but not the point. Then how can I...
  32. C

    Proving Thermodynamics equations using partial derivatives

    Homework Statement Prove (∂V/∂T)_s/(∂V/∂T)_p = 1/1-(gamma) (gamma = Cp/Cv) Homework Equations (∂V/∂T)_s = -C_v (kappa)/(beta)T (where beta = 1/V(∂V/∂T)_p, kappa = -1/V(∂V/∂P)_T C_v= - T(∂P/∂T)_v(∂V/∂T)_s The Attempt at a Solution As part(a) ask me to find C_v, I do it similar for...
  33. N

    Chain rule and partial derivatives

    Homework Statement Suppose the differentiable function f(x,y,z) has the partial derivatives fx(1,0,1) = 4, fy(1,0,1) = 1 and fz(1,0,1) = 0. Find g'(0) if g(t) = f(t2 + 1, t2-t, t+1).Homework Equations The Attempt at a Solution Ok I'm given the solution for this and I'm trying to work through it...
  34. J

    Calculating Derivatives and Traces to Solving for det(I + tA) = tr(A)

    Hey guys, any hints on how to show that \frac{d}{dt}|t=0 det(I + tA) = tr(A) ? I did it for 2x2 but I can't figure out a generalization. Thanks
  35. M

    Derivatives& the Slope of the Graph: Inflection Point

    Homework Statement For the function f(x)=(x^2-3)/(x-2), determine the locations of any points of inflection, if any
  36. M

    Derivatives & the Slope of a graph

    Homework Statement Given Homework Equations The Attempt at a Solution
  37. S

    Finding Power Series Representation of Derivatives: 1/x-9

    how can i find a power series representaion of d/dx (1/x-9)
  38. L

    Understanding Lie Derivatives: Acting on Vectors & Tensors

    I've been trying to get a grasp on Lie Derivatives. I understand that we can represent a lie derivative acting on a vector as a commutator. What do I do when I act a lie derivative on a tensor? Can I still just write out the commutator?
  39. R

    Multi Calculus- Partial Derivatives

    Homework Statement I am translating the question from another language so it might not be word to word with the original question. assume x(s,t) and y(s,t) determined by these two functions: sin(xt) +x+s=1 eyt+y(s+1)=1 The following function is defined H(x,y)=x2+y2-xy such that...
  40. Q

    Confused about derivatives of the metric

    Hi, I am incredibly confused about second derivatives of the metric. I know that in general, the covariant derivative of a vector is given by \nabla_a v^b = \partial_a v^b + \Gamma^b_{ac}v^c and I think I understand how to generalize to higher rank tensors (just decompose into an...
  41. H

    Chain rule for partial derivatives

    If I have u = u(x,y) and let (r, t) be polar coordinates, then expressing u_x and u_y in terms of u_r and u_t could be done with a system of linear equations in u_x and u_y? I get: u_r = u_x * x_r + u_y * y_r u_t = u_x * x_t + u_y * y_t is this the right direction? Because by...
  42. V

    Product Rule with Partial Derivatives

    Hi, so I'm trying to solve Laplace's equation by separation of variables, and there's a basic step I'm not understanding with regards to the product rule. Given A product rule (i think) is taken to make the first term easier to deal with and we get I'm just having trouble...
  43. H

    Finding Derivatives Using Taylor/Maclaurin Polynomials

    Homework Statement Compute the 6th derivative of f(x) = arctan((x^2)/4) at x = 0. Hint: Use the Maclaurin series for f(x). Homework Equations The maclaurin series of arctanx which is ((-1)^n)*x^(2n+1)/2n+1 The Attempt at a Solution I subbed in x^2/4 for x into the maclaurin...
  44. C

    Partial derivatives of composition

    Homework Statement Find the partial derivatives with respect to u,v of \bar{U}(\bar{x}(u,v)), where \bar{U} is the unit normal to a surface given by the parametrization \bar{x}(u,v). (This, of course, is part of a larger problem, but I just am looking for advice with the calculus.)...
  45. W

    Derivatives: Checking your work, how?

    Homework Statement I'm in Pre-Calculus this semester and it's going swimmingly and I thought I'd try and get ahead for Calc I, which I plan on taking this summer. Anyways, all I have really to go off of right now is "How to Ace Calculus: The Streetwise Guide", my brain, and wikipedia. I'm...
  46. C

    What Are the Solutions to These Calculus Problems?

    hints? Derivatives: Intervals, stationary points, logarithms, continuous functions Homework Statement Got any hints or anything? 1. Suppose that f(x) = (x - 3)^4 ( 2x + 5)^5 a) Find and simplify f ' ( x ) b) Find stationary points of f c) Find exactly the intervals where f is...
  47. T

    Derivatives in Economics problem

    Homework Statement The cost in dollars for producing x units is given by C(x) = 1.22x+ 2500 . The demand curve is given by p(x) = (60,000-x)/(10,000) A. Find the revenue function R(x) in simplest form. B. Find the marginal revenue function and the marginal revenue for selling 15000...
  48. T

    Please check work on derivatives lab

    Homework Statement Sorry about not using the template, but I didn't really see how I could have. If you guys/gals could please check over my answers to these questions and point out the ones I miss that would be outstanding. Thank you! 1. The position of an object moving on a coordinate...
  49. K

    Higher derivatives of exp(f(x))

    Homework Statement Suppose f: R -> R has derivatives of all orders. Prove that F(x) := exp(f(x)) also has derivatives of all orders. Homework Equations The Attempt at a Solution I can kind of see that this is true but am unsure about how to lay out a proof. Using the chain...
  50. A

    How can I use the Quotient Rule for derivatives to simplify my final result?

    I am still working on getting anything other than subscripts to post with my latex formatting, so for now I have posted a word document. Any help would be greatly appreciated, thanks. Joe
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