Find the limit $\lim_{x\to1}\left(\frac{\frac{\frac{e}{2}\left(e^{\left(x-1\right)}-1\right)}{x}x}{x-1}\right)$

Find the derivative

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

Find the derivative

$\frac{d}{dx}\left(\pi100^2=0\right)$

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

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