If $f(x)=3 x^2+2 x f^{\prime}(1)+f^{\prime \prime}(2)$,then $f(x)=$ . . . . . .

If $y = x \left[ \left( \cos \frac{x}{2} + \sin \frac{x}{2} \right) \left( \cos \frac{x}{2} - \sin \frac{x}{2} \right) + \sin x \right] + \frac{1}{2\sqrt{x}}$,then $\frac{dy}{dx} = $

Find the derivative of the function $\sin^{n} x$ with respect to $x$,where $n$ is an integer.

$\frac{d}{d x}\left(e^{\log _e \sqrt{1+\tan ^2 x}}\right) =$

Let the function satisfy the equation $f(x+y)=f(x)f(y)$ for all $x, y \in \mathbb{R}$,where $f(0) \neq 0$. If $f(5)=3$ and $f^{\prime}(0)=2$,then $f^{\prime}(5)$ is

If $f(x)=|x-5|+|x+5|+|x-4|+|x+4|$,then $\frac{f^{\prime}(1)-f^{\prime}(-6)}{f^{\prime}(-1)+f^{\prime}(6)}=$