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Math Help - definition of a derivative

  1. #1
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    definition of a derivative

    Find lim  (3^(2+h)^2)-81/h.
    h->0

    *Should be 3 raised to the (2+h)^2, not (3) (2+h)^2*


    How do I solve this? So f(x)= 3^(x^2), f'= a^x =a^xlna

    I got: f'(2)=3^(2^2)(ln3)=81(ln3)
    Key says: 324(ln3).
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  2. #2
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    Quote Originally Posted by hazecraze View Post
    Find lim  (3^(2+h)^2)-81/h.
    h->0

    *Should be 3 raised to the (2+h)^2, not (3) (2+h)^2*

    How do I solve this? So f(x)= 3^(x^2), f'= a^x =a^xlna
    I got: f'(2)=3^(2^2)(ln3)=81(ln3)
    Key says: 324(ln3).
    Chain rule!

    f(x) = 3^{x^2} then f'(x) = 3^{x^2} \ln 3 \cdot 2x.
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