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D/dx(f(3x^5)) = 5x^3 calculate: f ' (x) [f prime of x]?

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D/dx(f(3x^5)) = 5x^3 calculate: f ' (x) [f prime of x]?

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  1. using the chain rule...

    f'(3x^5) *(15x^4) = 5x^3

    f'(3x^5) = 1/(3x).

    doing some manipulation you can see that...

    f'(x) = 1/fifthroot(3^4*x)

    if you plug 3x^5 in you can see you get 1/ (3X)

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