Solve the integral of logarithmic functions $\int\cot\left(t\right)\ln\left(5\sin\left(t\right)\right)dt$

Find the derivative

$\frac{d}{dx}\left(x^{-1\cdot \frac{3}{2}}\right)$

Find the derivative

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

Find the derivative

$\frac{d}{dx}\sqrt{x}$

Find the derivative

$\frac{d}{dy}\left(y^{\left(-1\right)\cdot\frac{1}{2}}\right)$

Find the derivative

$\frac{d}{dx}\left(x^{\frac{1}{2}}\right)$

Find the derivative

$\frac{d}{dx}\left(x^{\frac{1}{4}}\right)$

Compute the integral

$\int x\cdot\cos\left(x\right)dx$