If $f(x) = 10 \cos x + (13 + 2x) \sin x$, then $f''(x) + f(x)$ is equal to

If $y=x+\tan x$, then $\cos ^2 x \frac{d^2 y}{d x^2}+2 x$ is equal to

If $\sqrt{x+y}-\sqrt{x-y}=c$, then $\frac{d^2 y}{d x^2}=$

If the three functions $f(x)$,$g(x)$,and $h(x)$ are such that $h(x) = f(x) \cdot g(x)$ and $f^{\prime}(x) \cdot g^{\prime}(x) = c$,where $c$ is a constant,then $\frac{f^{\prime \prime}(x)}{f(x)} + \frac{g^{\prime \prime}(x)}{g(x)} + \frac{2c}{f(x) \cdot g(x)}$ is equal to:

If $f(x) = |x|^3$,show that $f''(x)$ exists for all real $x$,and find it.

If $y_k$ is the $k$-th derivative of $y$ with respect to $x$,and $y = \cos(\sin x)$,then $y_1 \sin x + y_2 \cos x$ is equal to