Question

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?

Answer 1

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)

Answer 2

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

Answer 3

I think you got it.

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