List of top Mathematics Questions on Logarithmic Differentiation asked in BITSAT

If $ y = \ln(x^2 + 1) $, then find $ \frac{dy{dx} $ at $ x = 1 $.
If $ f(x) = e^{2x} \sin x $, find $ f'(x) $.
Let $y = e^{2x}$ . Then $\left(\frac{d^{2}y}{dx^{2}}\right) \left(\frac{d^{2}x}{dy^{2}}\right) $ is
$\frac{d}{dx} (x^x)$ is equal to