Differentiation Definition and 1000 Threads

Hello again :) I get the feeling I'm missing some kind of 'trick', as this is proving a very difficult question :( I'll write out my frustration below; Homework Statement Find f'(x) if f(x) = \int^{cosh(x^{2})}_{0} tanh(t^2)dt Homework Equations --- The Attempt at a Solution My idea was...

Homework Statement when is this statement true : the derivative df/dg of the function f(g) exists what does this mean exactly? Homework Equations The Attempt at a Solution does it mean- 1. df/dg represents the rate of change of f with respect to g at any given value...

Homework Statement x^6 + y^6 = -6 I have to prove that y'' = 30x^4/y^11 Homework Equations The Attempt at a Solution Using implicit differentiation: 6x^5 + 6y^5 dy/dx = 0 6y^5 dy/dx = -6x^5 dy/dx = -x^5/y^5 Quotient Rule: [(y^5)(-5x^4) - (-x^5)(5y^4 dy/dx)] /...

Homework Statement I'm stuck halfway in my differentiation. The question is: Suppose f(x) is the following function when x > 0, find the x-coordinate of the critical point of f(x). Homework Equations Equation = f(x) = e^x - 5x^2 - ln(x) The Attempt at a Solution I solved for...

Hi there, I'm writing a research paper and have hit a roadblock, (wikipedia did not help) and one of my collaborators sent me an e-mail that I do not understand. I am attempting to find when the following functional is stationary: T = \int\limits_{\lambda_{1}}^{\lambda_{2}}...

the problem is to find y'' or d2y / d2x the equation is y2 = x2 first i found the first derivative dy/dx = 2x / 2y = x / y then i found the second using the quotient rule and got y'' = (y - x(dy/dx)) / y2 i plugged in y' into y'' and got y'' = (y - (x2/y)) / y2 but then I am...

In most of exercises of textbooks when ask me to differentiate f using logarithmic differentiation some time f(x) = 0 for some values of x , so I I used logarithmic Differentiation for all x in domain of f , such that f(x) not equal zero. then prove using the definition directly that for...

I'm having trouble understanding the proof/solution below (please see photo, I also wrote out the problem below). I highlighted the part of my problem in red (in the picture attached). Basically I'm not sure what identity they use to get the Kronecker delta after differentiating or whether they...

I've written a Levenberg-Marquardt nonlinear optimization routine that employs the reverse-mode automatic differentiation algorithm for building the Jacobian. So far it has worked marvelously for me. However, now I have to use functions that contain integrals that cannot be analytically taken...

It's been years since I've done maths properly so I'm rusty with it. I'm helping out a colleague at work who is studying maths for an OU course. Homework Statement Part 1: Differentiate function. f(x) = e^(0.5x+cos(x)) Part 2: Use answer from part 1 to show. g(x) =...

Homework Statement In general I havn't had problems using the differentiation rules until I came on this question, I'm probably doing something stupid any help is handy. Plugged it into an online differentiation solver and it comes up with (x^2-1)/(x^2) which I am getting nowhere near to in my...

Problem I'd like to prove \frac{d}{dt}[\frac{\partial}{\partial{x}}f(x(t),y(t),t)]=\frac{\partial}{\partial{x}}[\frac{d}{dt}f(x(t),y(t),t)]. Attempt \begin{equation*}\begin{split} \frac{d}{dt}[\frac{\partial}{\partial x}f(x(t),y(t),t)]=\frac{d}{dt}\lim_{\epsilon\to...

Homework Statement Let p be a polynomial function with p(a)= 0 =p'(a) for some real a. Which of the following must be true? A) p(x) is divisible by x+a B) p(x) is divisible by x^2+a^2 C) p(x) is divisible by x^2-a^2 D) p(x) is divisible by x^2+2ax+a^2 E) p(x) is divisible by x^2-2ax+a^2...

How might I make my script perform differentiation on a user-defined function? I also want the function and its derivative (in the form of a function) to be applied throughout the script, say in the forms of f and f' respectively, which I believe requires str2func. Example: The user is...

Homework Statement How could one apply differentiation formulas on this one: \partial^{2}\left(2sinh(nx)\div\sqrt{sinh(2L)-2L}\right)\div\partial x^{2} Homework Equations The Attempt at a Solution is this differentiation formula enough to differentiate:

Homework Statement I sat my calculus exam at the end of june and of the questions on the paper required us to find the extreme values of the following equation: g\left(x,y\right) = \left(x-1\right)\left(y-1\right)\left(x^{2} + y^{2} -2\right) The Attempt at a Solution So i get...

Consider the partial differential of Q to the power of n w.r.t. x. How would you rearrange this expression so that it contains a partial derivative of Q w.r.t. x?

First I attempted to ipmlicitly differentiate c2 = a2 + b2 -2abcos(theta) da/db I almost got the correct solution according to MIT's key, however I missed one part. The cos from the original function remained cos, and I had differentiated it to -sin. I'm just wondering why it...

Homework Statement (3x+2)^5.(x+1)^-2 Homework Equations dy/dx = dy/du . du/dx The Attempt at a Solution y=(3x+5)^5 . (x+1)^-2 u = 3x + 5 , du/dx = 3 v = u^5 , dv/du = 5u^4 = 15(3x+5)^4 u = x + 1 , du/dx = 1 v = u^-2 , dv/du = -2u^-3 -2(x+1)^-3 dy/dx = 15(3x+5)^4 ...

The coefficient of rigidity n of a wire of length L and uniform diameter is given by: n = AL/d^4 where A is a constant...If errors of +- 0.25% and +-1% are possible in measuring L and d respectively, find the maximum possible error in the calculated value of n... how do i do this...

Homework Statement find the d^2y/dx^2 if y^3 + y = 2 cos x at the point (0,1) Homework Equations The Attempt at a Solution my dy/dx = (-2 sin x)/(3y^2 + 1) I don't know how to find d^2y/dx^2? And when and how will I use the oint (0,1)?

Homework Statement Consider the curve satisfying the equation 2(x+1)^(tanx)=(y^2)cosx+y and find dy/dxHomework Equations (tanx)'=sec^2x (lnx)'=1/xThe Attempt at a Solution I've tried taking the natural log of both sides and then taking d/dx of both sides but something seems to go wrong with...

http://img838.imageshack.us/img838/8007/given01.jpg http://img220.imageshack.us/img220/52/given2r.jpg Actually that should be the square root of -2X

Homework Statement A plane flying with a constant speed of 300 km/h passes over a ground radar station at an altitude of 1 km and climbs at an angle of 30 degrees. At what rate is the distance from the plane to the radar station increasing a minute later? Homework Equations a2+b2=c2The...

Homework Statement Prove that \frac{d}{dz}z^n = nz^{n-1}\;\;\; \forall n\in\mathbb{N} using the Product Rule for differentiation and mathematical induction. Homework Equations \frac{d}{dz} f(z) = \lim_{\Delta z\to 0} \frac{f(z+\Delta z) - f(z)}{\Delta z} \frac{d}{dz}[f(z)g(z)] = f\,'(z)g(z) +...

Homework Statement Find dy/dt, given: y=x^2-5x+1 x=s^3-2s+1 s=\sqrt{t^2+1} 2. The attempt at a solution I am trying to use the chain rule for the case where y is a function of x, x is a function of s and s is a function of t, like below...

I don't think I fully understand implicit differentiation. I have read my textbook and watched many videos, and I think I will get an A on my test on this solely by memorizing the rules, but I would really like to understand this topic. From what I know, you are supposed to use implicit...

Homework Statement x^{3}y + y^{3}x = 30 Homework Equations - The Attempt at a Solution My understanding is that I'm supposed to take the derivative of each side and try to solve for y'. But, I don't know how to treat the y when I am differentiating it, to a power or whatever...

I'm doing some work with neural networks lately and I'm having trouble with this seemingly simple equation. The equation describing the network is: y = \psi(W3 x \psi(W2 x \psi(W1 x I))) Where: y (scalar) is the output value W1 (2x2 matrix) are the 1st layer weights W2 (2x2 matrix) are...

I think I have found a formula for finding Successive derivatives of factorials, though it may have been found already. I have attached it to this post.

Homework Statement S = (8x^2 - 7x + 125)/(8x+7) Where the value of x is unknown The Attempt at a Solution u = 8x^2 - 7x + 125 du/dx = 16x - 7 v = 8x + 7 dv/dx = 8 ds/dx = (v*du/dx - u*dv/dx)/v^2 = (8x+7*16x-7 -...

Homework Statement s = 8sin(125t)e^-7t Where the value of t is unknown The Attempt at a Solution u = 8sin(125t) du/dt = 1000cos(125t) v = e^-7t dv/dt = -7e^-7t ds/dt = v*du/dt + u*dv/dt = (e^-7t *...

Homework Statement Use implicit differentiation to find dy/dx 2x^3+x^2y-xy^3 = 2 Homework Equations Chain Rule et al. The Attempt at a Solution My questions is this. When deriving something like xy^3, apply the product rule to get 1y^3 + x\frac{d}{dx}y^3 I am confused on...

The problem I am having with these is that I'm sometimes not sure whether to begin differentiating first, or to start taking logarithms - and whether the order changes the outcome For example: Find the equation of the tangent line to the curve at the given point. y= \frac{(e^x)}{x}...

Given an equation in the form 0 = ax2 + bx + c, why is it not possible to simply differentiate both sides, and produce 0 = 2ax + b, and solve for x, instead of going through the drudgery of the quadratic equation? My knowledge of calculus tells me that it is because 0 = ax2 + bx + c is not a...

Hello, I'm working on some problems and I want to pose the following, though I am not completely sure it is correct. Can somebody point me to some sources on this? I have tried googling myself, but I only found differentiation identities with either just vectors and scalars on the on hand, or...

Homework Statement I tried using D[x = y - y^2, x, NonConstants -> {y}] and it keeps telling me that y - y^2 is not a valid variable.

Find ∂fxand ∂fy for: f(x,y)=(3x2+y2+2xy)1/2 i tried using the chain rule and said f(x,y) = u1/2 then ∂fu = 1/2u-1/2, ∂ux = 6x + 2 and ∂uy=2y+2 ∂fx = 1/2(3x2 + y2 + 2xy)-1/2(6x + 2) ∂fy = 1/2(3x2 + y2 + 2xy)-1/2(2y + 2) im not sure if this is correct as i don't know if I am doing the ∂ux and...

Homework Statement Q1. using implicit diff to find dy/dx when x^2 y + 6xy^2 = 5x-2 Q2. Find max and min values of y= x^3 -3x^2 -6x + 7 on the interval -3<=x<=5 Q3.Find the exact values of the x coordinate of the points of inflexion on the graph of y = 2x^4 +3x^2 +x +5 Q4. a red car is...

Just wondering if I have done this correctly? Homework Statement Differentiate: x^{sin3x} The Attempt at a Solution x^{sin3x}=e^{sin(3x)ln(x) Employing chain rule. y=e^{u} u=sin(3x)ln(x) dy/dx = e^{u}\times(sin(3x)/x + 3ln(x)cos(3x)) Final Solution? = dy/dx =...

Good afternoon, This is not actually a homework question; it's for self-study. I'm reading a Calculus book, and one of its exercises asks the following: If xnym = (x+y)n+m, show that xDxy = y (where Dxy is the derivative of y with respect to x). The only way I could think of to get the correct...

Hello guys Let y = x^i x is real, i imaginary, then is it right to say: y' = ix^{i-1} and must y be real?

All I know about Leibnitz is \frac{d^{n}}{dx^{n}}f(x) = \sum^{n}_{i=0} \left(\stackrel{n}{i}\right) g^{n-i}(x)h^{i}(x) and I don't understand what the answer sheet says: Parts of it perhaps - I can see they take the 0th, 1st and 2nd derivative, but why not more? I mean why stop at 2? I know...

I've been studying Turbulence, and there's a lot of averaging of differential equations involved. The books I've seen remark offhandedly that differentiation and averaging commute for eg. < \frac{df}{dt} > = \frac{d<f>}{dt} Here < > is temporal averaging. If...

Homework Statement d(x(t)2)/dt Homework Equations The Attempt at a Solution I guess that this should be: 2x(dx/dt) but I'm not sure how to justify it: u= x d(u2)/du = 2u (d(u2)/du)(du/dt) = d(u2)/dt So 2u(du/dt) = 2x(dx/dt) Is this right?

Hi, can someone help me solve this double derivative please: \frac{1}{c}\frac{d^2}{dt^2}\frac{1}{c^2t^2-x^2-y^2-z^2} I am assuming you get use the quotient rule but I am getting so many terms I am getting confused... Its in my notes and I am not quite getting it... Thanks

Question: y6 + 6 (x^2+4)6 = 9 6y5 .dy/dx . 6(x2 + 4)5 . (2x) = 0 6y5 .dy/dx = -6(x2+4)5 .(2x) dy/dx = 6y5 / -6(x2 + 4)5 .(2x) dy/dx = 6y5 / 12x(x2 +4)5 Although the answer is ment to have y5 as the numerator, not 6y5? ------------- Another Q. [Simplifying result from...

Homework Statement So here's a question from my textbook 'Calculus: Concepts and Contexts' 2nd ed. by James Stewart. This is section 3.6 # 54 We have Cartesian coordinates set up with an ellipse at x^2 + 4y^2 = 5 To the right of the ellipse a lamppost (in 2D!) stands at x=3 with...

I'm a self-learner (so far) when it comes to Calculus. I have completed College Algebra (with a grade of B) and PreCalculus (with a grade of A) and am a later-in-life than usual student (age 50). I plan on returning to College in January of 2012 and will start on a degree in either...

Homework Statement derive (s2t3) / (rs2t3) with respect to s The Attempt at a Solution equation becomes s2t3*(rs2t3)-1 which becomes s2t3r-1s-2t-3 then just differantiate like a polynomial? i tried this on an online partial differentiation calculator and it gave me an...