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Math Help - Finding F'(a) and G'(a)

  1. #1
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    Finding F'(a) and G'(a)

    Suppose and
    Also suppose

    Find

    and


    To be honest I really don't have any idea what its asking or more of what its giving me and how to use it. Any help will be great thanks.
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  2. #2
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    Hello, UMStudent!

    This is an exercise in handling the Chain Rule.


    Suppose: .F(x) = p(x^9) .and .G(x) = [p(x)]^9

    Also suppose: .a^8 = 6, .p(a) = 2, .p'(a) = 13, .p'(a^9) - 15

    Find: .(a) F'(a) .and .(b) G'(a)

    (a) We are given: .F(x) .= .p(x^9)

    Differentiate: .F'(x) .= .p'(x^9) 9x^8

    Then we have: .F(a) .= .p'(a^9) 9a^8
    . . . . . . . . . . . . . . . . . . . . . . . .
    Substitute: . . . F(a) .= . . .15 9 6 . = . 810


    (b) We are given: .G(x) .= .[p(x)]^9

    Differentiate: .G'(x) .= .9[p(x)]^8 p'(x)

    Then we have: .G'(a) .= .9[p(a)]^8 p'(a)
    . . . . . . . . . . . . . . . . . . . . . . . . .
    Substitute: . . . G'(a) .= .9 (2^8) 13 . = . 29,952

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  3. #3
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  4. #4
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    great, thanks alot for all your help.
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