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Math Help - Derivatives - using differentiation rules

  1. #1
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    Derivatives - using differentiation rules

    Hi can some more knowledgeable than I please check my work?

    Calculate the derivative using the differentation rules

    a)

    f(x) = (4x^4 - (2/5)x^3)^1/4

    f'(x) = 1/4 (4x^4 -2/5x^3)^-3/4 (16x3-(6/5)x^2)


    b)

    f(x) = e^-5x + 3tan4x)^5

    f'(x) = 5(e^-5x+3tan4x)4(-5e^-5x+12sec^2)

    c)

    f(x) = √(cosx + √x^7)

    f'(x) = 1/2 (cosx + x^7/2)^-1/2 (-sin + (7/2)x^5/2)


    I appreciate your help

    Thanks
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  2. #2
    Junior Member
    Joined
    Feb 2009
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    Scotland
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    The first one is fine.

    Question b) provided the bracket you missed is at the beginning of the function and it is  f(x) = (e^{-5x} + 3\tan 4x)^5 your answer is correct but I think you made a typo at the end where it should have  12\sec^2 4x you missed the  4x .

    The third one is also fine.

    I understand it can be confusing when using the chain rule and you can doubt yourself whether you've done it right but you managed it all well by yourself.
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