The derivative of $f(x) = 3|2 + x|$ at the point $x_0 = -3$ is

Find the derivative of the following function: $5 \sec x + 4 \cos x$.

Find the derivative of the following function: $\frac{a}{x^{4}}-\frac{b}{x^{2}}+\cos x$,where $a$ and $b$ are fixed non-zero constants.

If $f(x)=x^{n}$, where $n$ is a non-negative integer, then the values of $n$ for which $f^{\prime}(\alpha+\beta)=f^{\prime}(\alpha)+f^{\prime}(\beta)$ for all $\alpha, \beta > 0$ is:

The solution set of $f'(x) > g'(x)$,where $f(x) = \frac{1}{2} (5^{2x+1})$ and $g(x) = 5^x + 4x \ln 5$ is:

If $y = f \left( \frac{2x - 1}{x^2 + 1} \right)$ and $f'(x) = \sin x$,then $\frac{dy}{dx} = $