Differentiation Definition and 1000 Threads

Use Implicit Differentiation to find y" if xy + y - x = 1 so far i got 1y + dy/dx - dx/dx = 1/dx then i did y + y' - 1 = 0 y' = 1-y i don't understand how to get the y" . i don't think i even have y' done right!

Homework Statement A research studied the commercial fishing situation in a certain fishing zone. Denoting the total catch of corel fish in that zone in t years time from January 1, 1992 by N(t) (in thousand tonnes), he obtained the following data: t=2, N(t)=55 t=4, N(t)=98 The...

Homework Statement A vehicle tunnel company wants to raise the tunnel fees. An expert predicts that after the increase in the tunnel fees, the number of vehicles passing through the tunnel each day will drop drastically in the first week and on the t-th day after the first week, the number...

Hello again! This time I have another calculus question for you, coming straight out of my study of the free Schrodinger equation, since I am not that experienced with that kind of derivative. It all starts with a given wavefunction (which I think is 2-dimensional,correct me if wrong)...

y = (sinx)2x LNy = 2xLN(sinx) + (1 over sinx)(cosx)(2x) Answer y' = (sinx)2x [2cosx over sinx + 2xcotx] and y = (cosx)cosx i did it the same way as above Answer i got was y' = (cosx)cosx [ (-sinx)(cosx) + sinx] am i anywhere right?

I have a basic question about taking partial derivatives. Say I have a function of 3 variables and i want the derivative of only one. Do I take the derivative of the one variable and HOLD THE OTHER TWO CONSTANT? Or, do I take the derivative of the variable and TREAT THE OTHER TWO AS...

y = (sin2x)3(x4-4x)6 divided by (cosx) + e3x i came out with an answer y' = (sin2x)3(x4-4x)6divided by (cosx) + e3x [3cot2x + 24x3-24 divided by x4-4x + Tanx + 3x could someone tell me if I am right? i don't know if this is what I am supose to do, if you want me to write out...

Homework Statement Differentiate y = \left(\frac{x+2}{\sqrt[3]{x}}\right)3 Homework Equations -Chain Rule -Quotient Rule -Power Rule -Product Rule? The Attempt at a Solution First I got rid of the fraction by taking the negative of x^3, and then used the chain rule to differentiate...

Homework Statement Prove that \frac{dy}{dx}=\frac{y}{x} for \sqrt{\frac{x}{y}}+\sqrt{\frac{y}{x}}=10 x is not equal to y which is not equal to 0 The Attempt at a Solution Tried all the normal methods but none seem to work...anyone have any ideas?

Homework Statement The curve y = ax^{2} + bx passes through the point (2,4) with gradient 8. Find a and b . I have no idea how to work out a and b , do I use simultaneous equations? Homework Equations The Attempt at a Solution I have no idea how to work out a and b , do I use simultaneous...

Homework Statement Find derivative of y with respect to x. Sin(xy) = Sinx Siny Homework Equations The Attempt at a Solution Use chain rule (product rule for inner function) to differentiate the left. Use product rule to differentiate the right and I get the following...

Homework Statement I am trying to differentiate log((x+(x^2+y^2)^0.5)/(-x+(x^2+y^2)^0.5)) with respect to y Homework Equations I know that d/dx of ln(x) = 1/x but i am getting really confused when it comes to differentiating wrt to y? Can I have some help please! The Attempt at a...

1. Homework Statement , attempt at a solution Please see attached. I'm actually busy with a physics problem, but solving it requires that I complete this part correctly. It's straightforward differentiation, but I think I made an error with my signs somewhere and I can't for the life of me...

Homework Statement In polar coords: y = rsin(\theta) y' = dy/dt = r'sin(\theta) + rcos(\theta) \theta' If I want \partial r' / \partial y' can I just solve for r' and take the derivative of y'? so \partial r' / \partial y' = 1 / sin \theta I am hoping this is incorrect because...

if u(x,t)=ae^-gx sin(nt-gx) where A,g and n are const.,and partial derivative of u w.r.t t= a^2[(partial derivative w.r.t x(partial derivative of u w.r.t x)] show :(1/a)[n/2]^1/2=g

given that z=[x^2 tan^-1(y/x)]-[y^2 tan^-1(x/y)].find value of [z][xy]. where [z][xy] stand for partial derivative w.r.ty(partial derivative of z w.r.tx)

Homework Statement differentiate y = (3x2-4)1/2+(x2+4)1/2 with respect to x Homework Equations y = (3x2-4)1/2+(x2+4)1/2 The Attempt at a Solution dy/dx = (3x2-4)1/2dy/dx+(x2+4)1/2dy/dx Is it correct...? for the first part let u = (3x2-4)1/2 du/dx = 6x y = u1/2 dy/du = 1/2u-1/2 dy/dx =...

Homework Statement 1. Calculate the gradient of the curve y = 2x3 - 5x2 + 46x + 87 at the point where it crosses the x-axix. 2. Show by differentiation and solving a quadratic equation, that there are no points on the above curve where the gradient is zero.Homework Equations y = 2x3 - 5x2 +...

Homework Statement Consider y = 2a + ax find dy/dx dy/dx = a That is right is it not, as a is treated merly as a constantNow consider this question: Use the substitution y = vx to transform the equation: dy/dx = (4x+y)(x+y)/x² into x(dv/dx) = (2+v)² According to the mark scheme they...

i am given two differentiable function f and g . prove that for u(x)=max(f(x),g(x)) and v(x)=min(f(x),g(x)) there is one sided derivatives ??how to put mim ,max functions into the formula of derivative formula?? f'(x)_+ = \lim_{h \to 0^+} \frac {f(x + h) - f(x)}h (one-sided derivative...from...

Homework Statement Use logarithmic differentiation to find the derivative of the function. Homework Equations y = (sin(x))^(ln(x)) The Attempt at a Solution I guessing the first step is raise both sides to "e", but so far I have only completed problems by taking the natural log...

suppose f is a continues function on point x_0 prove that g(x)=(x-x_0)*f(x) differentiable on x_0?? calculate g'(x_0) i tried to think like this: if f(x) is continues on x_0 then lim f(x) as x->x_0 equals f(x_0) mvt says f'(c)=[f(a)-f(b)] cauchys mvt says...

Homework Statement What is the integral of: y + x \frac{dy}{dx} The Attempt at a Solution I know that it is xy, after implicit differentiation. However, I cannot get it without prior knowledge of implicit differentiation.

Homework Statement Find the derivative of the following function f. Homework Equations f(x)=x^log(x) The Attempt at a Solution I really don't know how to do this, as it's x to the power of a function of x.

Homework Statement Given two quantum preparations \frac{1}{\sqrt{2}} \left( |0\rangle + | 1 \rangle \right) \frac{1}{\sqrt{2}} \left( |0\rangle - | 1 \rangle \right) Give a measurement that will distinguish between these two preparations with high probability. The Attempt at a...

Hey I'm stuck on a problem, i have to find the differential of y=5x(2x-1)^3 and therefore find the x-coordinate of a stationary point on a graph, I use the chain rule and get the differential to be 30x(2x-1)^2 and therefore the x-coordinate to be 0.5 however my textbook says the differential...

Hey guys I am having a bit of trouble solving the following problem, differentiate y = x ((1+x)^0.5) I am using the product rule however I am getting a different answer to the back of my textbook I was wondering if anyone could help clear this up for me, thanks.

Let f be continuous on [0,1] and differentiable on (0,1) such that f(0)=f(1), prove that there exist a 0 < c < 1 such that f\acute{}(1-c) = -f\acute{}(c). thanks for any suggestions.

Homework Statement Let y = tan2(3x-2) Find dy/dx The solution is: 2*tan(3x-2)*sec(3x-2)*3 = 6*tan(3x-2)*sec2(3x-2) Why is it not: 6*tan(3x-2)*sec(3x-2) I am thinking: y = (tan(3x-2))2 take the power 2 down,multiply with the parentes multiply with the defferentiated parentes...

I'm trying to understand how Randall and Sundrum go from Eq. (9) to Eq. (10) in their RS1 paper: http://arxiv.org/abs/hep-ph/9905221 I understand that since the extra dimension \phi is periodic, we must have \frac{d^2}{d\phi^2}|\phi|\propto \delta(0) - \delta(\phi - \pi). However...

Homework Statement If y^2 - 2xy=21, then dy/dx at the point (2,-3) is ? Homework Equations y^2 - 2xy=21 The Attempt at a Solution I know that I have to differentiate the function. I just do not know how to do it: implicitly or explicitly.

Homework Statement Define f(0,0)=0 and f(x,y)=\frac{x^{3}}{x^{2}+y^{2}} if (x,y)!=(0,0) Let \gamma be a differentiable mapping of R1 into R2, with \gamma(0)=(0,0)\;and\; |\gamma'(0)>0|. Put g(t)=f(\gamma(t)) and prove that g is differentiable for every t in R1 Homework Equations...

Homework Statement suppose f is a differentiable mapping of R1 into R3 such that |f(t)|=1 for every t. Prove that f'(t)\cdot f(t)=0. I guess it is more proper to write (\nabla f)(t) \cdot f(t)=0, where (\nabla f)(t) is the gradient of f ant t. Homework Equations The Attempt at a...

So we are given T(t) = c'(t)/||c'(t)|| as well as ||T|| = 1 We also know T(t)dotT(t) = 1 and T'(t)dotT(t) = 0 The problem asks us to find T'(t) I tried differentiating c'(t)/||c'(t)|| treating ||c'(t)|| as the square root of the dot product of c'(t) with itself. I used the product...

Homework Statement Suppose A is a real nxn matrix and f: R^n --> R is definted by f(v)=v^tAv (where v^t denotes the transpose of v). Prove that the derivative of f satisfies (f'(v))(w) = v^t (A+A^t)w Homework Equations The Attempt at a Solution I'm kinda lost here and I really...

Homework Statement The problem reduces the derivative (dZ/d(1/V)) to (dZ/dV) x (dV/d(1/V)), where Z is the compression factor and v is molar volume. It further shows that it equals -V^2(dZ/dV). I don't know how they arrived at that value because by my logic it should be 1/(-V^2)...

hi, I want to know the practical use of Integration and Differentiation. I know what it is. I just want to know how can i explain it with a practical example. example : for Differentiation - the dy/dx can be explained that y is dependent on independent variable x. How can d2y/dx2 be...

Homework Statement find d^2y/dx^2 at (1,1) for: x^2y + x^2 -y^2 = 1 Homework Equations none The Attempt at a Solution i worked it all out but the answer I am getting is not an option. could someone show me where i made a mistake? I am not asking you to do the problem for me...

Hi, I'm confused about what differentiation on smooth manifolds means. I know that a vector field v on a manifold M is a function from C^{\infty}(M) to C^{\infty}(M) which is linear over R and satisfies the Leibniz law. This should be thought of, I'm told, as a 'derivation' on smooth...

Homework Statement Let f be continuous and differentiable on [a,b], and suppose that f attains its maximum and minimum points c and d, respectively, where c,d belong to [a,b]. Show that f ' (d) = 0 Homework Equations The Attempt at a Solution I thought about using the Mean...

I am having trouble remembering the correct approach here. This is in regards to deriving a governing equation for conservation of momentum for a non-Newtonian fluid. I thought about posting in engineering, but it is more of a calculus question: d/dx(((-dv/dx)^(m-1))*(dv/dx)) where we are...

I was looking at results of different numbers in the equation \sqrt[x]{x} and found out that the biggest result came when it was \sqrt[e]{e}. I know this can be re-written as x^{1/x} and that the gradient would be 0 at x = e. How would you differentiate y = x^{1/x}, I can't seem to do it using...

Can I differentiate a complex function, like e^{-if(t)}?

Homework Statement For the function of two variables f(x,y)=tan^-1(y/x) find df/dx and df/dy I know i just differentiate with respect to x and then to y but I'm stuck on the tan^-1(y/x) I know tan^-1(x)=1/1+X^2 when I applied this with respect to x I get 1/-1+y I think this is wrong...

I saw the argument for complex differentiation today and I had a question about a 'well known' aspect of the argument. My professor said something like this (at least a version of it): Derivatives on complex variables are defined in the usual way. However, in the complex plane, delta(z) may...

Homework Statement Show using cartesian components that d/dt(a.b)=(da/dt).b+a.(da/dt) The Attempt at a Solution a= axi+ayj+azk b=bxi+byj+bzk a.b=axbx+ayby+azbz d/dt(a.b)= d/dt(axbx+ayby+azbz)

Homework Statement A man 6 feet tall walks at a rate of 5 feet per second toward a streetlight that is 30 ft high. The man's 3 ft tall child follows at the same speed, but 10 feet behind the man. At times, the shadow behind the child is caused by the man, and at other times, by the child...

Homework Statement Let Δf= d^2f/dx^2+ d^g/dy^2 (laplace equation - Partial Derivatives) Show Δ(f(g(z))= Mod(g'(z))^2 * Δf(w,v) where g(z)=w(x,y)+v(x,y)i Homework Equations we propably need to use cauchy riemman equations: dw/dx = dv/dy and dw/dy = - dv/dx and chain rule The Attempt...

Homework Statement what is the implicit differentiation ? Homework Equations 2sin(x)cos(y)=1 The Attempt at a Solution d/dx[2sin(x)cos(y)]= d/dx[1] 2cos(x)*-sin(y)*dy/dx=0 I haev a bad feeling i did this wrong...

hi i couldn't solve this question i think there is a mistake in it anyone can check it please ? http://img296.imageshack.us/img296/3716/13055173zr3.png