Differentiating Definition and 262 Threads

Homework Statement A curce has equation: x² + 2xy - 3y² + 16 = 0 find the co-ordinates of the points on the curve where dy/dx = 0 Homework Equations The Attempt at a Solution I don't have a clue. Do I convert them into parametric equations?

Homework Statement Differentiate y = u * e^t + v * t * e^t Homework Equations Product Rule. The Attempt at a Solution y = u' * e^t + u * e^t + ( v' * t * e^t + v * e^t + v * t * e^t) u and v are functions of t. I forgot whether the product rule works like this: d/dt [xyz] =...

Hi I have a question about rearranging the following equation (I saw this in a finance book): If we rearrange and differentiate Z(t;T) = e^{-\int_{t}^{\tau}r(\tau)d\tau} We get r(T) = -\frac{\partial}{\partial{T}}(\log{Z(t;T)}) My question is: how do we differentiate...

Homework Statement How fast is the area of a square increasing when the side is 3 meters in length and growing at a rate of 0.8meter/minute? Homework Equations SA=LW L=3 dL/dt=0.8 The Attempt at a Solution I have no clue how to start this and I'm bad at word problems.

Homework Statement U is a function of x and t d/dt(U) = d/dx(U) + V(x,t)U U(x,0) = f(x) Suppose: U(x,t) = e^(Integral from 0 to 1 [V(x+s,t-s)]ds) * f(x+t) Show directly (no change of variables) that this solves the above PDE Show using change of variables that this solves the...

Can anybody recommend a good site to bone up on differentiating and integrating ln and e functions?

[SOLVED] need some help differentiating Uh my bad, forgot how to differentiate ln's Homework Statement \frac{V_0}{xln(\frac{b}{x})} Find dE/dx I can almost get the answer, but I had to use MATLAB to find the actual answer, so I am kind of feeling stupid now. My problem is when...

Homework Statement Find dw/dt. Check result by substitution and differentiation w = (x^2 + y^2)^1/2, x = e^2t , y = e^-2tHomework Equations The Attempt at a Solution dx/dw = x/(x^2 + y^2)^1/2 dy/dw = y/(x^2 + y^2)^1/2 Dont really know where to go with it

I'm confused about differentiating an improper integral. Consider the function F(r)=\int_0^\infty J_0(rx)\,dx=\frac{1}{r}\int_0^\infty J_0(m)\,dm=\frac{1}{r} where I've solved the integral by making the substitution m=rx (I think this is OK). Now I would like to find \frac{\partial...

When is it valid to differentiate both sides of an equation? I was working on a physics problem and came across this, where I had to solve for p(r). q(r) = \int_0^r \rho(s) * 4 \pi s^2 ds = \frac{Q r^6}{R^6} So, differentiating both sides with respect to r and using the Fundamental Theorem...

Hello, I was set the problem to differentiate the following streamfunction in order to find its x and y velocities: psi=psinought*tanh(y/d)+mu*exp(-((x-L)^2+y^2)/2*sigma^2)*cos(k(y-vt)). Being the lazy sort I am, I called in Maple. dpsi/dx worked out perfectly (in that I got the same...

1. Differenciate the following functions i) y = x2ln(4x) ii) y = ln (x + 1)/x iii) y = ln (x2 - 1)1/22. Laws for differentiating logs and exponentials 3. I did some of the more easy one's, these ones just got me stumped. i) i think you would use the product rule. so u = x2 and v =...

Notation: I^x means the integral sign from 0 to x Question: Let f be a smooth function. Prove that d/dx [I^x f(x,y)dy] = f(x,x) + I^x (d/dx)f(x,y)dy using the chain rule for derivatives (do NOT use Leibnitz's rule for differentiating an integral). I don't know how to express I^x...

Homework Statement Differentiate: v = 2at x + 3bt^2 y + cz w.r.t time to get a where x, y and z are unit vecotrs and should have hats above them Homework Equations The Attempt at a Solution I get a = 2a x + 6bt y + z But I am not sure if that z should completely...

Homework Statement \int_{x}^{2\,{x}^{2}+1}sin{t}^{2}dt I need to take differential of that Homework Equations Fundamental theorem of calculus The Attempt at a Solution I know 't' is a dummy var, so I replace it with x, and then get sin((2x^2+1)^2)-sin(x^2) as answer. But I am not very...

Homework Statement differentiate f(x)= x^x^x Homework Equations chain rule product rule The Attempt at a Solution x^x (lnx) i don't know what to do after this

Homework Statement Differentiate using the Chain Rule: y=\cos^2(\frac{x^2 + 2}{x^2 - 2})Homework Equations The Attempt at a Solution y' = -2\cos(\frac{x^2 + 2}{x^2 - 2})\sin(\frac{x^2 + 2}{x^2 - 2}) [\frac{2x(x^2 - 2) - (x^2 + 2)2x}{(x^2 - 2)^2}] \mbox{derivative of cos is -sin so I brought the...

Please HELP...Differentiating Inverse Functions Homework Statement f(x) = x^3 + 2x - 1 when a=2 2. The attempt at a solution I thought you did... 1/(f '(f-1(x))) but I am not sure how to solve for x? 0=x^3 + 2x - 1 1=x^3 + 2x -1 I tried factoring but that did not work either.

d/dx[t/(1+t^2)^(1/2)] The answer say 1/(1+t^2)^(3/2) I can tget that for the life of me. Used product rule and I can't seem to simplify it I come up with 2/(1+t^2)^(3/2) Where does the 2 go? This is for a principal unit vector problem so a quick solution is all i need. thanks

differentiating double integrals -- help please! Hello, Could somebody please help me with my problem? I have a double integral F(t) = Integral from 0 to t of f(s,t). w.r.t. d(g(s)) f(s,t) = Integral from t to A of h(s,u). w.r.t. d u. Where "g(s)" is a function of "s", which may or...

Hi, everyone, I'm new here and don't know how to type mathematics, but I have a scanner. I have a function L_A and it is an integral. I want to differentiate this function with respect to A. I already have the answer written but what I don't know is how it was obtained. Just by...

Given: \begin{array}{l} x = 2\cos t \\ y = 2\sin t \\ \end{array} find \frac{{dy}}{{dx}} I started by finding dy/dt and dx/dt \begin{array}{l} \frac{{dy}}{{dt}} = 2\cos t \\ \frac{{dx}}{{dt}} = - 2\sin t \\ \end{array} Now, dy/dx = (dy/dt) / (dx/dt)...

Its funny.. because I got this right on a test.. but.. I'm looking back at it.. and it doesn't make sense how I figured it out... I had to find the IC of d(\frac{x^2}{y}) this was my work... d(\frac{x^2}{y}) = 2xy - x^2y^2 - y^2 d(\frac{x^2}{y}) = \frac{2xy - x^2y}{y^2} I'm just confused...

Homework Statement I would like some help on differentiating the lorentz factor with respect to time Homework Equations The Attempt at a Solution i arrived at (-1/2) (1-v^2/c^2)^{-3/2} but a forum on this website says it is (-1/2) (1-v^2/c^2)^{-3/2} ( \frac{-2v}{c^2} dv/dt)...

differentiating with respect to... I have a question on differentiating the function z/(2x + y) with respect to x. Is the answer -2z/(2x + y)^2 ? Thanks:smile:

How do you go about differentiating rcos$ with respect to time...? In the book I am studying from it says d$/dt d/d$ (rcos$) is the process to find the answer... but what does this mean...?

Homework Statement Use the product rule to show that dx^n-1/dx = (n-1)x^n-2 Homework Equations The general idea is.. If: h(x) = f(x)g(x) Then: dh(x)/dx = f(x)dg(x)/dx + g(x)df(x)/d(x) The Attempt at a Solution It seems like a simple solution but everytime I attempt solving it...

f(t) = (1+tan t)^(1/3) differentiate using chain rule. u = 1 + tan t y = u^(1/3) dy/dt = dy/du x du/dt u=1+tan t 1/3 u^(-2/3) when u = 1 + tan t x sec^(2)t = = sec^(2)t/3(1+tan t)^(2/3) Did I do this correct??

\int_{-\infty}^{infty} s e^{-\frac{2s^2}{N}} ds how do i integrate here?? I don't think the 'trick' of differentiating wrt N would work here since the limits of integration are all space... any ideas??

Hi all, I hope everyone is well and that life is treating you all good. I am going to be honest with my question and say that I have not tried to do it myself yet. I, unfortunately, do not have time now to try and then repost so I do hope you will all forgive me for just stating a...

Can someone point me to a reliable source (textbook, website) that teaches this technique? It seems like no course at my university covers this technique even though it is quite useful for solving particular integrals!

Hey, Is it possible to differentiate x^x? I’ve tried with the use of logs, but it doesn’t seem to work…….any help would be kindly appreciated :smile: Thanks, Pavadrin

Hey. If i have: y = 2x\sqrt {4 - 2x^3 } To differentiate it, i used the product rule, but used the chain rule to differentiate the \sqrt {4 - 2x^3} part. I got the answer right, but was just wondering, is there a quicker way of doing it? Or have i gone about it the right way? Thanks...

a question i couldn't get the right answer to: Differentiate 1. y= 3^x (log(3) x) [3 = base (dont know the right syntax for typing up logs on the web)] what i have so far: y = 3^x (ln 3) (log(3) x) + 3^x / xln3 right...

Differentiate the function: f(u) = e1/u So, I used the chain rule and figured out that f '(u) = (-u-2) e1/u My question is, why do you have to use the chain rule? I know that if f(x) = ex then f '(x) = ex Why can't I pretend that 1/u is x and then say that f '(x) = ex = e1/u In...

1. differentiate the volume of a cylinder with v respect to h my working out: v= πr^2h dV\dh= 2πr n da answer is not right how do i make da "h" remains in da equation? could some one please help me? thank you

Hi all, I was just wondering if anyone knew how to differentiate Bessel functions of the second kind? I've looked all over the net and in books and no literature seems to address this problem. I don't know if its just my poor search techniques but any assistance would be appreciated.

Hello Calculus Forum, I need some help in differentiating piecewise functions and finding local/absolute minimum/maximum values. Problem is, I don't know how. For example, ...[/color]-x , if x<0 f(x)={ 2x^3-15x^2+36x , if 0<x<4, or x=0, or x=4 ...[/color] 216-x , if x>4my first...

Well actuallly 2 thms. They have to do with homogeneous functions. f(tx1,...,txn) = t^k * f(x1,...,xn). Now how do you show A) d/dx1 f(tx1,...,txn) = t^k-1 * d/dx1 f(x1,...,xn) and B) kt^(k-1)*f(x1,...,xn) = x1*d/dx1 f(tx1,...,xn) + xn*d/dxn f(x1,...,xn) A) In the book They say that...

let f(x) = ln(x-2)+ln(x-6). Write down the natural domain of f(x). i got this bit right, it's x>6 find f'(x) i got 1/(x-2) + 1/(x-6) which i think is right. then it says find the intervals for which f'(x) is a. positive and then b. negative. for a. i put f'(x)>0 and solved...

Before we differentiate, we must know whether a variable in that expression represents a constant or variable, correct? For example, if we have the function, f(x) = r^3 x^2 f'(x) = \frac{d}{{dx}}\left[ {r^3 x^2 } \right] (1) Now if r represents a variable then, f'(x) = r^3 \cdot...

d/dx(y*x^2)=x^2/(1+x^2) I guess I can't write this as: dyx^2=x^2dx/(1+x^2) dy=dx/(1+x^2) beacuse I don't get the right answer... So what do I do?

I need to differentiate D (the first equation). In this equation, there is an arcsin. I am not sure what to do about this. Well . . . just have a look: http://www.mlowery.0nyx.com/differentiate.jpg" If the browser says access denied, copy and paste the URL into a new browser window and it will...

I've had troubled sleep because of this...:cry: I tryed a lot and got this... Can you spot any mistakes or give me hints on how to approach this Thanks

I have been happilly solving away a multitude of different questions until the book threw me this curve ball...10^(3x) My first attempt was as follows: let y=u^3 and u=10^x dy/du = 3u^2...du/d10 = x(10^(x-1))...3x(10^2x(10^(x-1)))...3x(10^(3x-1)) the answer given in the book however is...

I'm having some trouble differentiating x^{\sqrt x } . I know that the derivative of x^{\sqrt x } probably begins with x^{\sqrt x } \cdot \ln (x) \cdot \frac{1}{{2\sqrt x }} but once the base is also x then there is probably more to it than that. Anyone?

How can I use trig identities to let me differentiate \sin \left ( x + \frac{\pi}{2} \right) and 3 \sin x - 2 \cos x?

[SOLVED] differentiating [ sin(1/ln(x)) / x ].. solution? hello all. I do not have the solution to this question that I am about to ask. But if you find the time, try this solving this problem and feel free to type your answer and compare with mine. differentiate :: sin(1/ln(x)) / x my...

What are the rules for differentiating tan, sin & cos? I know cos = -sin tan = sin/cos?

Hello I have made a simple spline(x,y) of 4 datapoints and I want to differentiate it. I can't get it to work; I have tried fntlr, fnder ect. Can anyone help? Karin