Find the derivatives of the functions.f(x)=e^{\ln x}-e^{2ln(x^{2})})

${\displaystyle f\left(x\right)=e^{\ln x}-e^{2\ln \left(x^2\right)})}$
Apply ${\displaystyle {\ln a}^n=n\ln a}$
$f(x)=e^{\ln x)-e^{ln(x^2{)}^2}}$ Apply ${\displaystyle {\left(x^m\right)}^n=x^{mn}}$
${\displaystyle f\left(x\right)=e^{\ln x}-e^{{\ln x}^4}}$
Recall that $\ln e^z=z$, so
${\displaystyle f\left(x\right)=x-x^4}$
Differentiate both sides with respect to x
${\displaystyle f^{\prime }\left(x\right)=\frac{d}{dx}[x-x^4]}$
Therefore,
$f^{\prime }(x)=1-4x^3$