Differentiation Definition and 1000 Threads

implicit differentiation help :) again! Homework Statement Use implicit differentiation 1) x/(y-x2)=1 and 2) (y2-1)3=x2-y The Attempt at a Solution 1) x/(y-x2)=1 => [(y-x2)(1)-(x)((1*dy/dx)-2x)]/[(y-x)2]2=0 => y-x2-x(dy/dx)+2x2=[(y-x)2]2 I think I'm going to stop here because I'm pretty...

Homework Statement Find the points (if any) of of horizontal tangent lines on : x2 + xy + y2 = 6 Homework Equations n/a The Attempt at a Solution So far I've concluded that I must find the points at which dy/dx = 0. I've solved for dy/dx and arrived at dy/dx = (-2x-y)/(x+2y)...

Homework Statement If (sqrt x) + (sqrt y) = 11 and f(9)=64 ---> find f '(9) by implicit differentiation The Attempt at a Solution I keep getting lost in my work here... first, taking derivative of both sides: d/dx ((sqrt x) + (sqrt y)) = d/dx (11)...

Homework Statement If f(x) = 2sin(x) + (4x)^x find ---> f ' (3) Homework Equations d/dx (e^u) = e^u du/dx The Attempt at a Solution Here is my attempt: f(x) = 2sin(x) + e^(ln(4x)^x) = 2sin(x) + e^(xln4x) = d/dx (2sin(x)) + d/dx (e^(xln4x)) = 2cos(x)...

Homework Statement Hi can anyone tell me what is the derivative of this function. Homework Equations p(t) = u(X(t), t) The derivative of p with respect to t The Attempt at a Solution dp/dt = du/dX * dX/dt + 1 ?? or is it going to be du/dX * dX/dt

I just started learning Implicit Differentiation and came across an issue. I took the derivative of the circle function: y2 + x2 = 1 y' = -x / y This all made sense until I solved the circle function for y, which gives: y = \pm\sqrt{1 - x^2} For any x > 1, it's going to be complex. So, does...

Homework Statement Where does the graph of 25x^2 + 16y^2 + 200x - 160y + 400 = 0 have a horizontal tangent line. Homework Equations dy/dx dx/dy or something not sure. The Attempt at a Solution Well I know that a horizontal tangent line would mean the slope is zero...but what...

Homework Statement Find \partial x / \partial z at the point (1, -1, -3) if the equation xz + y \ln x - x^2 + 4 = 0 defines x as a function of the two independent variables y and z and the partial derivative exists. Homework Equations The Attempt at a Solution x + y/x \partial x...

How do you differentiate : 2^n/2? You can't you just use the power rule? The correct answer is 2^n/2 (In^2) 1/2 lg^2 x n Where lg is log base 2. The correct answer is 2lgn 1/n^2 . 1/n Why is this so? Isn't lg^2 = 1? And differentiate n and we get 1? Sorry if I sound...

implicit differentiation help :) Homework Statement Find dx/dy by implicit differentiation (x2+ y)2+ x2+ xy2= 100Homework Equations The Attempt at a Solution I'm trying to use the chain rule to solve it... i got The derivative ofb(x2+ y)2+ x2+ xy2= 100, with respect to x, is 2(x2+...

Let me first say i just learned implicit differentiation (earlier today) and i am also new in general to derivatives. I am finding implicit differentiation difficult but i want to understand it before we go over it in class. Homework Statement This is a example in my book. I have been trying...

Homework Statement (a) A belt of mass m per unit length is wound partly around a pulley. The power P(v) transmitted is given by P=Tv-mv3 where T is the tension and v is velocity of the belt. Use differentiation to show that the maximum transmission occurs when v=sqrt(T/3m). Homework...

Homework Statement find y' given x3+y2+x+y=2 Homework Equations The Attempt at a Solution dy/dx=3x2+2y(y')+1+y' I know that's wrong because my 89 gives it as y'=(-3x2+1)/(2y+1), I don't know how to get there though and what happened to the =2. Thanks

Homework Statement 2XY = Y^2 prove that y''2 = \frac{y^{2}-2xy}{(y-x)^3} EDIT: Sorry, don't know how to insert a space in Latex. Homework Equations The Attempt at a Solution 2y+2x \frac{dy}{dx} = 2y \frac{dy}{dx} \frac{dy}{dx}(2y-2x) = 2y \frac{dy}{dx}= \frac{y}{y-x}...

Homework Statement Find the equation of the tangent to the curve y = x2(x + 1)4 at the point P(1,16) Homework Equations The Attempt at a Solution dy/dx x2(x + 1)4 = (x + 1)3((x + 1)2x + 4x2) = (x + 1)3(6x2 + 2x) = (x + 1)3(2x)(3x + 1) Subst. 1 into find grad. (1 +...

Homework Statement differentiate: yx = y / sqrt(x2 + y2) Homework Equations The Attempt at a Solution I solved this problem by taking the ln of both sides and then solving. It seems from the context of the problem set that this was supposed to be easier than that. Am I...

Homework Statement Homework Equations The Attempt at a Solution I don't understand how they get from step 4 to step 5. Wouldn't you factor a cos x out of the brackets then have (\cos x)(1-\frac{1}{6}) to the left of the brackets. Then you can multiply the (1-\frac{1}{6}) inside...

Homework Statement Differentiate Homework Equations see 1. The Attempt at a Solution btw the x in the second equation is meant to be an r how much did i fail? :(

Implicit differentiation, what's going wrong!? Hey people can someone point out to me please where I'm going wrong with part B of this question, can't get it to look the answer in the book, d2y/dx2 = -3(x^6/y^7)- 3(x^2/y^3). My answer is listed below under part B section, but i can't...

Homework Statement dV/dT = 0.15(300-V) V is the volume of water in a container at time T. The rate of water flowing into the container is constant at 45 units^3/s. The rate of water leaking is proportional to the volume of water currently in the container. Find the volume of water in the...

Homework Statement Find the coordinates of the points on these curves at which the gradient has the given values. y=1/3x^(3/2)-x^(1/2), gradient=3/4 The Attempt at a Solution Basically the problem I have isn't really finding the answer because... x^(1/2)-x^-(1/2)=6/4[/b] and...

Homework Statement \frac{d}{dx} [ arctan (2x-3) ] The Attempt at a Solution The general solution for d/dx arctan(x) = \frac{du/dx}{1+x^2} so \frac{du/dx}{1+(2x-3)^2} du/dx = 2 \frac{2}{1+(2x-3)^2} \frac{2}{1+2x^2-12x+9} \frac{2}{10+2x^2-12x} now this is where my question...

Homework Statement Suppose g(x) = \int_0^x f(t) dt, where f is Lebesgue integrable on \mathbb R. Give an \epsilon - \delta proof that g'(y) = f(y) if y\in (0,\infty) is a point of continuity of f. Homework Equations The Attempt at a Solution I know I need to show that f(y) =...

Homework Statement a=(t^2 + 1)i - j + tk Find da/dt I multiplied out the brackets so a= it^2 + i - j + tk then got as far as da/dt= 2it + 0 + 0 + ? a) is this right so far? b) how do i integrate tk with respect to t? Any help would be greatly appreciated.

Can someone show me why the derivative of k(x) = cot x Is k'(x) = -cosec^2 x And not k'(x) = -1/tan^2 Thanks!

Hi, quick question. I have an inline function I would like to differentiate symbolically in Matlab, however when I do it I get the following: say x = inline('cos(t.^2)','t') ; xp = inline(char(diff(x(t),sym('t'))),'t') ; xp(t) becomes -sin(t^2)*t however I really...

Homework Statement I have a graph of velocity vs time and was asked "Describe how the velocity changes over the time interval of the problem" how do I do this all I have is the graph that is not defined by a function... well I can make my own strangely all it is is a bunch of linear lines...

Homework Statement Find d2y/dx2 for cos y + x2 =12 The first derivative I think is correct but the second I am unsure of, this is Q5 of 10 in an assignment and every other question has been far cleaner and easier making me think that I've missed something. We don't have to use implicit...

Homework Statement Find the equation of a tangent line at the curve at point (-3√3, 1) x^(1/3) + y^(1/3) = 4Homework Equations Point-slope: y-1=m(x-1) The Attempt at a Solution I took the derivative of that equation and resulted in -y^(2/3)/x^(2/3) When I tried plugging in x and y to...

Homework Statement If z² = x² + y² and dx/dt = 2 and dy/dt = 3 Find dz/dt when x=5 and y=12 Homework Equations I used The Attempt at a Solution But I resulted in: 2z dz/dt = 2x(dx/dt) + 2y(dy/dt) Plugged in x,y,dx/dt, and dy/dt to get: 2z (dz/dt) = 2(5)(2) + 2(12)(3) dz/dt = 80/2z...

Homework Statement If y = x³ + 2x and dx/dt = 5, find dy/dt when x = 2. The Attempt at a Solution I'm not really sure how to solve this problem at all. It's the first I've seen like this so I don't know what approach I should take.

Homework Statement Find an equation of the tangent line to the curve at the given point. y = ln(xe^(x²)) P=(1, 1) The Attempt at a Solution I know how to plug in the numbers into the Point-Slope formula once I find the derivative of the function, or slope, I'm just not sure...

Homework Statement see attachment- have to do this because i can't figure out how to do the notation in this part sorry... I have no idea where to go with this and probably need quite a bit of help with it--- thanks. Homework Equations The Attempt at a Solution

Homework Statement for the question and attempt see the attachment. I've nearly done this but from my ti-89 I know that i am missing a 2x from the top line and i can't find where its gone. been a while since I've done this and i think that its just a simple mistake... ps it does want the...

Homework Statement A conical tent must contain 40\pi ft^{3}. Compute the height and radius of the tent with minimal total surface area. (Include the floor material.) Homework Equations 1. \frac{\pi r^{2} h}{3} = 40\pi 2. \pi r \sqrt{r^{2} + h^{2}} + \pi r^{2} = S 3. \frac {dr}{dh} =...

can someone show me step by step how to find dy/dx of y=1/(x+y) using implicit differentiation?

I need to check my results on this integration find dy/dx if y=x^y I find: dy/dx= y^2/[x(1-yln(x))]

Hello. I was wondering if you have a complex function f: A \subset C \to C everywhere differentiable on A, can you say anything about the existence of \frac{d Re(f)}{d z} or \frac{d Im(f)}{d z}? I was thinking that it's easy to proof that if f : A \subset R \to C, then Re(f) and Im(f) are...

An example of implicit differentation in Stewart, 6th ed, p 883, is given as follows: x^3 + y^3 + z^3 + 6xyz = 1 Differentiating to find dz/dx, 3x^2 + 3z^2(dz/dx) + 6yz + 6xy(dz/dx) = 0 where the product rule was used to differentiate 6xyz with respect to x. Why isn't the...

Homework Statement I've been reading a textbook on tensor analysis for a while. The book uses the conclusion of "covariant differentiation commutes with contraction" directly and I searched around and found most people just use the conclusion without proof.Homework Equations For example...

1. I'm pretty sure I've got this right.. just needing a check. Cheers! 2. x^2+2xy-y^2+x^2=2 3. 2x+2x(dy/dx)+2y-2y(dy/dx)+2x=0 2x(dy/dx)-2y(dy/dx)=-4x-2y dy/dx(2x-2y)=-4x-2y dy/dx=(-4x-2y)/(2x-2y)

Homework Statement I am using Crank–Nicolson to solve a logistic function, modeling population growth. To get the next time step, I have to solve a quadratic equation. The problem is that i get two solutions for y(i+1). Does it mean that I am doing it wrong? If not, can I just pick the...

Homework Statement The curve C has equation y=k x^3-x^2+x-5 where k is a constant. A) Find the derivative of the function with respect to x The point A with x-coordinate -\frac{1}{2} lies on C. The tangent to C at A is parallel to the line with equation 2 y-7 x+1=0 . Find...

Consider the power series (n=1 to infinity) \Sigma (x^n)/(n*3^n). (a) Find the radius of convergence for this series. (b) For which values of x does the series converge? (include the discussion of the end points). (c) If f(x) denotes the sum of the series, find f'(x) as explicitly as...

Find the derivative of the following: y = 1/ COS(t^2) Homework Equations Here is my attempt Using (Cos(t^2))^-1 SOlve using the chain rule: u = t^2 du = 2t dy/dt = -1.(-sin(u))^(-2) .(2t) = -2t(-sin(u))^(-2) = -2t/(Sin(t^2))^2 Is this correct...

If xlny - y = 5e then find the value of dy/dxat the point(6e,e) Homework Equations So here is my attempt at the solution, please any advice on where I am going wrong or if indeed it is correct greatly appreciated xlny - y - 5e Therefore dy/dx is: x/y + lny - 1 -5e Substituting...

Homework Statement What is the Importance of Cell Differentiation in the formation of tissue? Homework Equations N/A The Attempt at a Solution I know that cell differentiation is the process in which a generic cell develops into a specific type of cell, but could you please explain...

In the process of deriving .\nabla^2u(x,y). in polar coordinates I am confuse how to work through the steps. The first step from the book is to find \frac{\partial u}{\partial x} Standard partial differentiation is at follow: \frac{\partial u}{\partial x} = \frac{\partial u}{\partial r}...

f: (0,+inf)->R and f(x) is 0 if x is irrational 1/n if x is rational (n is positive integer) For each rational and irrational, i want to show continuity/discontinuity of f Intuitively, i think at each rational f is discontinuous, and at each irrational f is continuous, but i...

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...