$\frac{d}{dx}\left(x^{ln\left(x\right)}\right)$
$\frac{d}{dx}\left(x^{sin\left(x\right)}\right)$
$\frac{d}{dx}\left(cosx\right)^x$
$\frac{d}{dx}\left(x^{4x}\right)$
$\frac{d}{dx}\left(\cos\left(x\right)^x\right)$
$\frac{d}{dx}\left(x-1\right)^{\cos\left(2x\right)}$
$\frac{d}{dx}\left(x^{cos\left(x\right)}\right)$
The limit of a function f(x) when x tends to infinity is the value that the function takes as the value of x grows indefinitely.
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