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.
Homework Statement
A) if http://www4d.wolframalpha.com/Calculate/MSP/MSP10819hf7feh5hf5hh7e00004ga728h1d42i6h0c?MSPStoreType=image/gif&s=18&w=161&h=20
Find the partial derivatives?
B) Suppose you are manufacturing blackboards and whiteboards and that P is your monthly profit when your...
Find the directional derivative of:
f(x,y) = (x^2)y-y^3, (2,1,3)
Can somebody explain to me why we did the step we did?
First we found the directional derivative of f(x,y,z)
▽f(x,y)
= <2xy, (x^2)-3(y^2), a>
▽f(2,1)
= <2(2)(1), (2^2)-3(1^2)), a>
= <2(2), 4-3, a> = <4,1, a>
and then we... did...
Homework Statement
h(t) = √t (1 - t^2)
Homework Equations
the product rule is (first) x (derivative of the second) + (second) x (derivative of the first)
The Attempt at a Solution
i've been working at this for a while. the closest answer i came up with was this:
h(t)= t^1/2 (t^1/2 -...
Homework Statement
2 problems.
1)
Find an example of a function f such that :
the line y=2 is a horizontal asymptote of the curve y=f(x)
the curve intersects the line y=2 at the infinitive number of points
2)
The position of an object moving along x-axis is given at time t by:
s(t)= 4t-4 if...
The Office of the US Currency Comptroller has an interesting chart 4 titled '5 Banks Dominate in Derivatives, Insured U.S. Commercial Banks, Second Quarter 2011'.
http://www.occ.gov/topics/capital-markets/financial-markets/trading/derivatives/dq211.pdf
I'm speechless!
Homework Statement
A metal bar of length l in the figure below has one end attached at a point P to a circle ofradius a < l. Point Q at the other end can slide back and forth along the x–axis.
(a) Find x as a function of θ (θ=angle POQ).
(b) Assume the lengths are in centimeters and the...
Homework Statement
This is a bonus problem on our homework, and I'm having trouble figuring out how to setup what I need.
Homework Equations
Here are my best guesses:
f_x=\frac{\partial f}{\partial x}
f_y=\frac{\partial f}{\partial y}
f_{xx}=\frac{\partial}{\partial...
The maximum rate of change of f at the given point and the direction in which it occurs.
f(x,y)=(y^2)/x, (2,4)
Answer: 4√2, <-1,1>
_________________________
For this problem, since I couldn't find the upside down triangle, I am going to use delta to represent the gradient of a function...
find the derivatives
of differentiation of trigonometric functions
1. y=cos(3x^2+8x-2)
2. y=tan^3 2x
3. y=sin5x sin^5 x
4. y=Square root of 4sin^2x+9cos^2x
help here please..
i can't understand trigonometric functions
sorry admin or moderator, i just search the net on how...
1. Hello there, I have a few questions on the derivative homework that I did but not sure if it's right or not. These are difficult and my teacher doesn't go over all of them so I don't know if it is right or not. Please help me so I can understand the concepts before the upcoming test.
1...
Hi to all of Physics forums community :),
I'm not sure whether or not I am in the right section. If not, I apologize for my mistake. Also, I am new to Calculus (I am in Cegep --> Quebec schooling system...) and I am taking Calculus 1 single variable. My teacher just started our class by...
Homework Statement
Hello,
My first post here
I have a numerical problem for Matlab but I get stuck with the basic math...
For a circuit I have three equations:
1.Inductance: L=Lo/(1+I^2)
2.Voltage over the inductance: V=L*dI/dt
3.Current over a condensator: I=-C*dV/dt...
In James Stewart's Calculus exercise 82 page 891 asks you to show that:
\frac{\partial P}{\partial V}\frac{\partial V}{\partial T}\frac{\partial T}{\partial P} = -1
I can do this by noting that V = \frac{nRT}{P} so that:
\frac{\partial V}{\partial T} = \frac{\partial}{\partial...
I have the PDE:
(v_r)^2+(v_z)^2=p^2 where v=v(r,z), p=p(r,z).
I have some boundary conditions, of sorts:
p=c*r*exp(r/a)exp(z/b) for some constants a,b,c, at r=infinity and z=infinity
p=0 at f=r, where
(f_r)^2=p*r/v-v*v_r
(f_z)^2=p*r/v+v*v_r
Is it possible that one could obtain an...
Homework Statement
cot^2(Cos\theta)Homework Equations
chain rule
f prime (x) = f prime(g(x) * g prime (x)
The Attempt at a Solution
I am not sure if I am just inputting the wrong numbers into webassign or I am just missing and important trig derivative and just completely off of the boat...
Homework Statement
Hi I'm just looking for a link to the proof of this theorem:
if the partial derivatives of function f exist and are continuous at a point then the function is differentiable there
Or even the name would be helpful
Its not a homework assignment per say, just something...
Hello, if I have a fundamental solution, ,f, to a partial differential equation L(f)=0, where L is the differential operator, is that true that the derivatives of the fundamental solution, like D(f), will also be solution to the partial differential equation?
Intuitively, is it because things...
Homework Statement
Suppose that the equation F(x,y,z) = 0 implicitly defines each of the three variables x, y and z as functions of the other two: z = f(x,y), y = g(x,z), z = h(y,z). If F is differentiable and Fx, Fy and Fz are all nonzero, show that
\frac{∂z}{∂x} \frac{∂x}{∂y} \frac{∂y}{∂z} =...
Homework Statement
The acceleration of a body is defined as a=-K*u^2 , K is const. When t=o sec V=Vo.
Find : a) V(t) b) X(t) c) V(x) .
Homework Equations
The Attempt at a Solution
Let a represent the area, p the perimeter, d the diagonal, b the breadth, and L the length of a rectangle. One can easily write down from analytical geometry all the various relationships between the above variables, and from these obtain directly a variety of partial differential quantities...
Homework Statement
\frac{d}{dx}e^{ax^{3}}
I'm simply trying to determine whether or not I am doing these correctly and applying the chain rule properly.
Homework Equations
Chain rule et al.
The Attempt at a Solution
\frac{d}{dx}e^{ax^{3}}
e^{ax^{3}}\frac{d}{dx}ax^{3}
e^{ax^{3}}a(3)x^{2}...
Homework Statement
I was messing around online when I found this: \frac{dy}{2} = 2x. This was derived from the function y = x2. I had never really seen anything like this before. When I solved for "dy," I got 4x. However, for example, when x changes from 0 to 2, the y changes from 0 to 4...
Homework Statement
If V=xf(u) and u=y/x, show that
x^2.d2V/dx2 + 2xy.d2V/dxdy + y^2.d2V/dy2= 0
(This a partial differentiation problem so all the d's are curly d's)
The Attempt at a Solution
I have tried to work out d2V/dx2 and the other derivatives, then multiply them by x^2 or 2xy or...
Hi,
Do you know the name of this kind of singularity at A ?
The function is finite but the left derivative is +\infty and the right derivative is -\infty.
http://shareimage.org/viewer.php?file=mt79897bbpxxse1v8pzb.jpg
Thanks
Dear Everybody!
I'm searching for some real life applications of partial derivatives. I would be very thankful, if you sent me some example.
Thanks from Hungary.
I have come to a bit of a misunderstanding with partial derivatives. I will try to illustrate my problem. Say we have a function f(x, y(x), y'(x)) where y'(x)=dy/dx. Now suppose that f does not explicitly depend on x. My physics book says at this point that ∂f/∂x=0, even though y(x) and y'(x)...
Homework Statement
Let f = f(u,v) where u = x+y , v = x-y
Find f_{xx} and f_{yy} in terms of f_u, f_v, f_{uu}, f_{vv}, f_{uv}
Then express the wave equation \frac{\partial^2f}{\partial x^2} - \frac{\partial^2f}{\partial y^2} = 0
Homework Equations
Chain rule, product rule...
What is the difference? I was pretty bored last night so I got onto Yahoo Answers and answered a few calculus questions. It was a simple integration by parts question:
\intxsin(x) dx
I solved as:
u = x
du = dx
dv = sin(x) dx
v = -cos(x)
uv - \intvdu
-xcos(x) + \intcos(x)dx =...
Homework Statement
y''+(1/y)*(y')2=0
Homework Equations
The Attempt at a Solution
This is another problem I am having trouble with. I have done searches around the internet, but seen that all "non linear" ODE of second order involves a non linear form in a non differential term...
URGENT !Year 11 Double variable derivatives
I am having trouble with this question it is derivatives. Previously I have been able to complete these with no trouble but am a little confused with how start this one:
y= a^2(3x+5)^3.
I don't know whether to use the product rule and just leave...
let C0 be the set of continuous functions f : R -> R. For n >= 1, let Cn denote theset of functions f : R -> R such that f is differentiable and such that f' is contained in C(n-1). (Therefore Cn is the set of functions whose derivatives f',f'',f''',...,f^(n) up to the nth order exist and are...
Hello, this question will essentially concern quantum field theory in curved spacetime, and it has two parts to it.
I have recently acquired DeWitt's treatment of the formalism, which immediately discusses the role of killing vectors in the theory. Specifically, given a killing vector field...
Hope this is the right section. I'm having trouble ironing out an apparent inconsistency in matrix trace derivative rules.
Two particular rules for matrix trace derivatives are
\frac{\partial}{\partial\mathbf{X}} Tr(\mathbf{X}^2\mathbf{A})=(\mathbf{X} \mathbf{A}+\mathbf{A} \mathbf{X})^T...
Homework Statement
Find all second partial derivatives of
z=arctan((x+y)/(1-xy))Homework Equations
d/dx of arctan(x) is 1/(1+x^2)The Attempt at a Solution
Not sure how to proceed... I don't want the answer, just an idea as to how to move forward.
My attempt at finding the first...
Homework Statement
Find the Derivative of:
(ln(cos4x)) / 12x^2
Homework Equations
y' ln(x) = 1/x
The Attempt at a Solution
I have determined the correct answer, but I am still confused as to how I came to the solution. Starting with the numerator, the derivative of cos...
Homework Statement
A man 6 feet tall walks away from a streetlight that is 18 feet tall. If the length of his shadow is changing at a rate of 3 feet per second when he is 25 feet away from the base of the light, how fast is he walking away from the light at this moment?
Homework Equations...
Let \varphi be a one-parameter group on a manifold M, and let f be a differentiable function on M, the derivative of f with respect to \varphi is the defined as the limit:
\lim_{t\to 0} \frac{\varphi^*_t[f]-f}{t}(x)=\lim_{t\to 0}\frac{f\circ \varphi_x(t)-f\circ...
Hi. Doing a bit of self study.
I would like to know how to understand the derivative. I understand the algebra and procedural stuff that you need to do to get the derivative of a function. Is there a way I can understand it graphically?
Say I draw y=x^2 on a graph. Then I draw y=2x on...
Homework Statement
1. The line perpendicular to the curve y = 2x^3 - x^2 + x - 3 at the point (1, -1) will intersect the x-axis at what point?
2. f(x) = |x^2 - 5| - x, for all x. Let g = f(f(f(x))), find g'(2). I tried just subbing in 2x - 1, the first derivative, to f(2x - 1) and...
Homework Statement
Let f(x) = axe^((bx)^2). Find the value for a times b if it's known that there's a max value of 2 at x = 3.
Second, There is one line which is tangent to the curve y = 1/x, at some point A and at the same time tangent to the curve x^2 at some point B. What is the...
Homework Statement
Let's say I have a function for a circle
x^2 + y^2 = C where C is a constant.
Then this is a cylinder with the z-axis.
Now in my ODE book, we would normally define it as
F(x,y) = C = x^2 + y^2 as a level surface.
Now my question is about what the partial...
Homework Statement
if f is infinitely continuously differentiable and f(0) = 0 then prove that all derivatives of f at 0 are 0 iff lim f(x)/x^n = 0 as x --> 0
Homework Equations
The Attempt at a Solution
I didnt know whether to use induction on this,
I tried a base case so...
Homework Statement
Find the general function f(x,y) that satisifes the following first-order partial differential equations
\frac{df}{dx}=4x^3 - 4xy^2 + cos(x)
\frac{df}{dy}=-4yx^2 + 4y^3
The Attempt at a Solution
I integrated both to get:
x^4 - 2x^2y^2 + sin(x) + c(y)
and
-2y^2x^2 + y^4...
Homework Statement
The position on the ground in the xy plane that is hit by the sun given by (x,y)=(3t+tan(phi), -2t+tan(theta)), where t, phi, and theta, are controlled input variables. What is the velocity of the hit point if the input variables are at values (5, pi/4, pi/3) and changing...
Something has been bugging as of late: usually, derivatives (ordinary and partial) are defined for interior points. However, I often come across statements in which they seem to also be defined for boundary points. For example, Leibniz' rule of integration, as usually stated, assumes some...