Posted by sh on Friday, October 29, 2010 at 10:06pm.
Find the derivative of
f(x)=x(14^x)
f'(x)=(14^x)+ (4^x)(ln4)(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) = (14^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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