If $f(1)=1$ and $f^{\prime}(1)=3$,then the derivative of $f(f(f(x)))+(f(x))^2$ at $x=1$ is

If $y(\alpha)=\sqrt{2\left(\frac{\tan \alpha+\cot \alpha}{1+\tan ^{2} \alpha}\right)+\frac{1}{\sin ^{2} \alpha}}$ for $\alpha \in\left(\frac{3 \pi}{4}, \pi\right)$,then find $\frac{d y}{d \alpha}$ at $\alpha=\frac{5 \pi}{6}$.

Let $f(x) = e^x$,$g(x) = \sin^{-1}x$ and $h(x) = f(g(x))$,then $h'(x)/h(x) = $

Differentiate the following with respect to $x$: $e^{x^{3}}$

If $y = \log(\sec(\tan^{-1} x))$ for $x > 0$,then the value of $\frac{dy}{dx}$ at $x = 1$ is:

The graph of function $f$ contains the points $P(1, 2)$ and $Q(s, r)$. The equation of the secant line through $P$ and $Q$ is $y = \left( \frac{s^2 + 2s - 3}{s - 1} \right) x - 1 - s$. The value of $f'(1)$ is: