List of top Mathematics Questions on Derivatives

If \( f(x) = \left(\frac{3+x}{1+x}\right)^{2+3x} \), then \( f'(0) = \)

If \( y = \sin^{-1}\left(\frac{1}{\sqrt{x+1}}\right) \) then \( \frac{dy}{dx} = \)

Find the value of \( \displaystyle \lim_{h \to 0} \frac{(a+h)^2 \sin(a+h) - a^2 \sin a}{h} \)