Prove the trigonometric identity $\frac{\cos\left(x\right)}{1+\sin\left(x\right)}=\sec\left(x\right)-\tan\left(x\right)$

Find the derivative

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

Find the derivative

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

Find the derivative

$\frac{d}{dx}\left(x\cdot \tan\left(y\right)\right)$

Find the derivative

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

Find the derivative

$\frac{d}{dx}\left(4\sin\left(x\right)\cdot \cos\left(x\right)\right)$

Find the derivative

$\frac{d}{dx}\left(5\cdot e^{7x}\cdot \cos\left(9x\right)\right)$

Find the derivative

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