If $y = \frac{\sqrt[3]{1 + 3x} \sqrt[4]{1 + 4x} \sqrt[5]{1 + 5x}}{\sqrt[7]{1 + 7x} \sqrt[8]{1 + 8x}}$,then $y'(0)$ is equal to

If $f(x) = \frac{e^{-x} \sin x}{\log_e x}$ and $f'(x) = f(x) \cdot g(x)$, then $g'(e) =$

If $f(\theta) = \cos \theta_1 \cdot \cos \theta_2 \cdot \cos \theta_3 \cdots \cos \theta_n$,then $\tan \theta_1 + \tan \theta_2 + \tan \theta_3 + \cdots + \tan \theta_n =$

If $y = \frac{x^2}{(x - 1)(x - 2)(x - 3)} + \frac{2x}{(x - 2)(x - 3)} + \frac{3}{x - 3} + 1$,then $\frac{xy'}{y}$ is equal to (where $y' = \frac{dy}{dx}$):

Differentiate the function with respect to $x$: $(\log x)^{x}+x^{\log x}$

Differentiate the function with respect to $x$: $(x \cos x)^{x} + (x \sin x)^{\frac{1}{x}}$