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Math Help - Derivation Question

  1. #1
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    Derivation Question

    Two Questions for the community:

    1) Let s(x) = x^(1/4), where x(t) = ln(f(t)) and f(t) is a differentiable function. Find ds/dt.


    2) Consider the function f(x0 = x^2 * e^(-x)

    Find the best linear approximation to f at x = 0, and compute the 2nd order Taylor polynomial at x = 0.

    I'm having problems with this question (I'm in Calc III and this is part of a long review sheet from Calc II; any help would be much appreciated)

    Cheers
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  2. #2
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    Quote Originally Posted by Sprintz View Post
    Two Questions for the community:

    1) Let s(x) = x^(1/4), where x(t) = ln(f(t)) and f(t) is a differentiable function. Find ds/dt.


    2) Consider the function f(x0 = x^2 * e^(-x)

    Find the best linear approximation to f at x = 0, and compute the 2nd order Taylor polynomial at x = 0.

    I'm having problems with this question (I'm in Calc III and this is part of a long review sheet from Calc II; any help would be much appreciated)

    Cheers
    1. Use the chain rule.

    \frac{ds}{dt} = \frac{ds}{dx}\,\frac{dx}{dt}.
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