Find the derivative using logarithmic differentiation method $\sqrt{3}\sqrt{15}\sqrt{\frac{1}{5}}$

Find the derivative

$\frac{d}{dx}\left(x^{2x+3}\right)$

Find the derivative

$\frac{d}{dx}\left(cos\left(x\right)^x\right)$

Find the derivative

$\frac{d}{dx}\left(x^{\frac{7}{x}}\right)$

Find the derivative

$\frac{d}{dx}\left(sinx^{lnx}\right)$

Find the derivative

$\frac{d}{dx}x^{e^x}$

Find the derivative

$\frac{d}{dx}x^{cosx}$

Find the derivative

$\frac{d}{dx}\left(x^{5\sin\left(x\right)}\right)$