Posted by **sh** on Friday, October 29, 2010 at 10:06pm.

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 -
**Reiny**, Friday, October 29, 2010 at 10:19pm
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 -
**sh**, Friday, October 29, 2010 at 10:27pm
So the negative is not included,

for example f(x)=-2^x

f'(x) would be (-2^x)(ln2)?

Thanks!

- Calculus -
**Reiny**, Friday, October 29, 2010 at 10:30pm
I think you got it.

in your example you could look at -4^x

as -(4^x)

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