The differential coefficient of $f(\sin x)$ with respect to $x,$ where $f(x) = \log x,$ is

Find the derivative of the function: $\frac{x^{2} \cos \left(\frac{\pi}{4}\right)}{\sin x}$

Let $f_1(x) = e^x, f_2(x) = e^{f_1(x)}, \ldots, f_{n+1}(x) = e^{f_n(x)}$ for all $n \geq 1$. Then for any fixed $n$, $\frac{d}{dx} f_n(x)$ is:

If $y = b \cos \log \left( \frac{x}{n} \right)^n$,then $\frac{dy}{dx} = $

Let $f(x) = x^m$, where $m$ is a non-negative integer. The value of $m$ such that the equality $f^{\prime}(a+b) = f^{\prime}(a) + f^{\prime}(b)$ is valid for all $a, b > 0$ is

If $y = \cos(\sin x^2)$,then $\frac{dy}{dx}$ at $x = \sqrt{\frac{\pi}{2}}$ is