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 $y=x^{n} \log x+x(\log x)^{n}$,then $\frac{d y}{d x}$ is equal to

If $f(0)=0$ and $f^{\prime}(0)=3$,then the derivative of $y=f(f(f(f(f(x)))))$ at $x=0$ is

If $y = x^2 + \cos(2x) + e^{ax}$,then find $\frac{dy}{dx}$.

Let $P$ be a non-zero polynomial such that $P(1+x)=P(1-x)$ for all real $x$ and $P(1)=0$. Let $m$ be the largest integer such that $(x-1)^m$ divides $P(x)$ for all such $P(x)$. Then,$m$ equals

The derivative of $\cosh^{-1} x$ with respect to $\log x$ at $x=5$ is