Suppose for a differentiable function $h$,$h(0)=0$,$h(1)=1$ and $h^{\prime}(0)=h^{\prime}(1)=2$. If $g(x)=h(e^{x}) e^{h(x)}$,then $g^{\prime}(0)$ is equal to:

Let $f(x) = x - 5$. If $g(x) = [f(4h(x) + 3)]^2$ and $h(1) = 4, h'(1) = -2$, then $g'(1) = .....$

If $f(x) = \sum_{p=1}^7 p^2 \sin^{-1}\left(\frac{4}{5} \sin(px) - \frac{3}{5} \cos(px)\right)$, then the value of $\frac{df}{dx}$ at $x = 1$ is (Given that $\sin^{-1}(\sin x) = x$)

If $f(x) = 2x^6 + 3x^4 + 4x^2$,then $f'(x)$ is:

Find the derivative of the following function: $\frac{\cos x}{1+\sin x}$

If $f:R \to R$ is a differentiable function and $f(1) = 4$,then the value of $\lim_{x \to 1} \int_4^{f(x)} \frac{2t}{x - 1} dt$ is: