If $y=a \cos (\sin 2 x)+b \sin (\sin 2 x)$,then $y^{\prime \prime}+(2 \tan 2 x) y^{\prime}$ is equal to

If $f(x)=\frac{x-1}{e^x}$,then $f^{\prime}(0)+f^{\prime \prime}(0)=$

If $y=\frac{2}{\sqrt{a^2-b^2}} \tan ^{-1}\left[\sqrt{\frac{a-b}{a+b}} \tan \frac{x}{2}\right]$,then $\left.\frac{d^2 y}{d x^2}\right|_{x=\frac{\pi}{2}}=$

If $f(x) = e^{(x+1)^n}; (n \in N)$,then the value of $n$ for which $f''(1) = 67(2^n e^{2^n})$ is

Let $f(x)$ and $g(x)$ be two functions having finite non-zero $3^{rd}$ order derivatives $f'''(x)$ and $g'''(x)$ for all $x \in R$. If $f(x)g(x) = 1$ for all $x \in R$,then $\frac{f'''}{f'} - \frac{g'''}{g'}$ is equal to

Find the second order derivative of the function $f(x) = x \cdot \cos x$.