Prove the trigonometric identity $\tan\left(x\right)+\cot\left(x\right)=\sec\left(x\right)\csc\left(x\right)$

Find the derivative

$\frac{d}{dx}\left(2x-1\cdot 4\cdot \ln\left(x+2\right)\right)$

Find the derivative

$\frac{d}{dx}\left(e^{8x}+4x+e^{8x}\right)$

Find the derivative

$\frac{d}{dx}\left(x^2-2x^5\ln\left(x+2\right)\right)$

Find the derivative

$\frac{d}{dx}\left(4\sec\left(x\right)-2\csc\left(x\right)\right)$

Find the derivative

$\frac{d}{dx}\left(e^{2x}-x\cdot \cos\left(xy\right)\right)$

Find the derivative

$\frac{d}{dx}\left(9x^4\cdot\ln\left(x^4\right)+\ln\left(x\right)^5\right)$

Find the derivative

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