Why the chain rule does not work for this question? 
$f(x)=x^{14x}$
Find $f'(x)$

I used the chain rule and wrote it as $f(U)=U^{14x},U(x)=x $, and get an answer :$14x(x)^{14x-1}$
But it is wrong .The right answer should be make $y=x^{14x}$ then $\ln y=\ln x^{14x}$  then $\ln y=14x\ln x$ then differentiate each side with respect to $x$ .
Can anyone explain why my method is wrong ?

There are two rules to use. The first $$(f^g)' = g\cdot f^{g-1} \cdot f'$$ if $g$ is constant and $$(f^g)' = \ln f \cdot f^g \cdot g'$$ if $f$ is constant. If neither are constant, the answer is the sum of both options:
$$(f^g)' = g\cdot f^{g-1} \cdot f' + \ln f \cdot f^g \cdot g'$$
This is also chain rule, but in a different form. You might have seen this pattern in product rule:
$$(fg)' = f'g+fg'$$
where you ferret out the dependence (derivative) in one function at a time. This is the intuition you can carry forward if you are careful about it.
