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Math Help - Derivative chain rule help

  1. #1
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    Derivative chain rule help

    Basically the Problem gives a table, but the way it words the problem kinda confuses me a bit:
    Suppose that the function f and g and their derivatives with respect to x have the following values x=0 and x=1
    x f(x) g(x) f(x)prime g(x)prime
    0 1 1 5 1/3
    1 3 -4 -1/3 -8/3
    (Sorry for the horribly made table)

    Evaluate the derivatives with respect to x of the following combinations at given value of x:
    a. 5f(x)-g(x), x=1
    b. f(x)g^3(x), x=0
    c. f(x)/(g(x)+1), x=1
    d. f(g(x)), x=0
    e. g(f(x)), x=0
    f. (g(x)+f(x))^-2, x=1
    g. f(x+g(x)), x=0

    Anyways you don't need to do all of them for me, like just explain how to do the first 2 would be enough, thanks.
    Last edited by maximade; October 18th 2009 at 04:35 PM. Reason: can u also do the 3rd and 4th one, im having a lot of trouble trying to figure this out
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  2. #2
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    Quote Originally Posted by maximade View Post
    Basically the Problem gives a table, but the way it words the problem kinda confuses me a bit:
    Suppose that the function f and g and their derivatives with respect to x have the following values x=0 and x=1
    x f(x) g(x) f(x)prime g(x)prime
    0 1 1 5 1/3
    1 3 -4 -1/3 -8/3
    (Sorry for the horribly made table)

    Evaluate the derivatives with respect to x of the following combinations at given value of x:
    a. 5f(x)-g(x), x=1

    From your table

     <br />
(5f(1)-g(1))' = 5f(1)'-g(1)' = 5\times \frac{-1}{3}-\frac{-8}{3} = \dots<br />
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  3. #3
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    For the first two, we have

    \frac{d}{dx}(5f(x)-g(x))=5\frac{d}{dx}f(x)+\frac{d}{dx}g(x)=5f'(x)+g'  (x).

    \begin{aligned}<br />
\frac{d}{dx}(f(x)g^3(x))&=\left(\frac{d}{dx}f(x)\r  ight)g^3(x)+f(x)\left(\frac{d}{dx}g^3(x)\right)\;\  ;\;\;\;\;\;\;\;\;\mbox{(Product Rule)}\\<br />
&=f'(x)g^3(x)+f(x)(3g^2(x)\cdot g'(x)).\;\;\;\;\;\;\;\;\;\;\mbox{(Power Rule, Chain Rule)}<br />
\end{aligned}
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  4. #4
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    Thats what I thought at first, but my friend said that u had to apply the chain rule?
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  5. #5
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    You do have to apply the chain rule in some of these questions.

    For d) and e) you need to.
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