Find the derivative using the product rule $\ln\left(2^x\right)=2^3$

$\frac{d}{dx}\left(\sqrt{\frac{x\left(x+2\right)}{\left(2x+1\right)\left(5x+3\right)}}\right)$

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

$\frac{d}{dx}\left(\ln\left(\mathrm{sech}\left(3x+8\right)\right)\right)$

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

$\frac{d}{dx}\left(\ln\left(1+x\right)\right)$

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

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