$\frac{d}{dx}\left(x^{lnx}\right)$
$\frac{d}{dx}\left(x^{x^2}\right)$
$\frac{d}{dx}\left(x^{\sqrt{x}}\right)$
$\frac{d}{dx}\left(x^{ln\left(x\right)}\right)$
$\frac{d}{dx}x^{\ln\left(x\right)}$
$\frac{d}{dx}\left(x^{2cos\left(x\right)}\right)$
$\frac{d}{dx}\left(x^{2x}\right)$
The logarithmic derivative of a function f(x) is defined by the formula f'(x)/f(x).
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