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Homework Help: Calculus; Derivatives

  1. May 21, 2012 #1
    Hi, I was hoping someone could help me out with my homework set.
    I have done alot of the questions, and it would help if someone could tell me if I have done them correctly. Thanks! :)

    Q1: Find first derivatives for the following functions
    Just wrote that out full for working, will shorten now
    (b) f(x,y)=x(y^3)+(2x^4)y
    (c) g(r,x,z)=rsin(zx)
    (d) e_(X1,X2....Xn)=sqrt(X1^2+X2^2....Xn^2)
    only write down one generalised partial derivative with respect to Xi
    I am not sure how to approach this one, help would be great
    I also am not entirely sure if I am somehow meant to put the two partial derivatives back together to get the complete first derivative?

    Q2: y(x,t)=Asin(kx-wt) where w=(pi/2), k=pi, A=5
    (a) find rate of change of y wrt to t at x=1, t=1
    (b) find rate of change of y wrt to x at x=(1/2), t=1

    If anyone could tell me if im on the right track with these questions, and help out with Q1 (d), I would be super appreciative.
    Last edited: May 21, 2012
  2. jcsd
  3. May 21, 2012 #2

    Ray Vickson

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    Homework Helper

    Your computation of g_t in (a) is incorrect; you need to use the Chain Rule to get a proper computation. You should have gotten [itex]g_t = 3 s t^2 \cos(st^3).[/itex] I did not check the others, so there may or may not be additional errors.

  4. May 21, 2012 #3
  5. May 22, 2012 #4


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    I'm glad you posted this link, as i just made it into my signature. Hopefully, it will help spread the message. :smile:
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