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Math Help - First and second derivative of e^6e^x?

  1. #1
    Junior Member BugzLooney's Avatar
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    First and second derivative of e^6e^x?

    derivative of e^6e^x?
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  2. #2
    Super Member General's Avatar
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    Quote Originally Posted by BugzLooney View Post
    derivative of e^6e^x?
    Is it e^{6e^x} ?
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  3. #3
    Junior Member BugzLooney's Avatar
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    Yes that is the question indeed.
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    The first derivate, using the chain rule

    f(x)=e^{6e^x}
    f'(x)=e^{6e^x} \cdot (6e^x)'
    f'(x)=6e^{6e^x} \cdot (e^x)'
    f'(x)=6e^{6e^x+x}
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  5. #5
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    consider the expression equal to say t. take logs on both sides of the equation then differentiate and u should get the derivative of t ie. the derivative of your expression.
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  6. #6
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    for the second derivative differetiate again as you already might be knowing!
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  7. #7
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    The second derivate

    f'(x)=6e^{6e^x+x}
    f''(x)=6e^{6e^x+x} \cdot (6e^x+x)'
    f''(x)=6e^{6e^x+x} \cdot (6e^x+1)
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  8. #8
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    Quote Originally Posted by BugzLooney View Post
    Yes that is the question indeed.
    If g is a differentiable function and f(x)=e^{g(x)}, then f is differentiable and:
    f'(x)=e^{g(x)} g'(x).
    Just apply this on your problem.
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