Calculus

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Find the derivative of
f(x)=x(1-4^x)
f'(x)=(1-4^x)+ (-4^x)(ln-4)(-4)(x)

ln can't be negative. Is the derivative correct?

  • Calculus -

    no, the second part of your product rule is not correct

    lets just differentiate
    1 - 4^x
    that would be (-4^x)(ln4)

    my final answer would be

    f '(x) = (1-4^x) + x(-4^x)(ln4)
    = 1 - 4^x - x(ln4)(4^x)

  • Calculus -

    So the negative is not included,
    for example f(x)=-2^x
    f'(x) would be (-2^x)(ln2)?
    Thanks!

  • Calculus -

    I think you got it.

    in your example you could look at -4^x
    as -(4^x)

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