If $f(1)=1$ and $f^{\prime}(1)=5$,then the derivative of $f(f(f(x)))+(f(x))^2$ at $x=1$ is

If $y = (\cos x^{2})^{2}$,then $\frac{dy}{dx}$ is equal to

Let $g(x) \neq 0, g^{\prime}(x) \neq 0, f(x) \neq 0, f^{\prime}(x) \neq 0$. If $F(x)=f(x) g(x)$, $G(x)=f^{\prime}(x) g^{\prime}(x)$, $F^{\prime}(x)=G(x) H(x)$, and $F^{\prime}(x)=F(x) K(x)$, then $H(x)+K(x)=$

Find the derivative of $\frac{x^{n}-a^{n}}{x-a}$ with respect to $x$,where $a$ is a constant.

If $f(x) = \frac{x}{1+|x|}$,for $x \in \mathbb{R}$,then $f^{\prime}(0)$ is equal to :

If $f(x)=\operatorname{cosec}^{-1}\left[\frac{10}{6 \sin \left(2^x\right)-8 \cos \left(2^x\right)}\right]$,then $f^{\prime}(x)$ is equal to: