Find the derivative using logarithmic differentiation method $\frac{d}{dx}\left(\frac{x^2-2}{-3}\right)$

Find the derivative

$\frac{d}{dx}\left(x^6+2\right)^x$

Find the derivative

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

Find the derivative

$\frac{d}{dx}\left(tan^{9-7x}\left(x\right)\right)$

Find the derivative

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

Find the derivative

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

Find the derivative

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

Find the derivative

$\frac{d}{dx}\left(1+\frac{7}{x}\right)^x$