I came across this question in my homework and am unsure why it works this way.
Given $y= \ln(e^{x^2})$, find the derivative.
The given answer work showed the formula rewritten as $y=x^{2}$ before starting the differentiation process. My thinking is because
$f(x)=\ln(x)$
And the inverse of the natural log function is $ f^{-1}(x)=e^x$
Am I right in thinking that multiplying the inverses cancel each other out? If so, why doesn't the x be removed, leaving the 2 as a constant?