Find the derivative of $(5x^{3} + 3x - 1)(x - 1)$.

Differentiate the following function with respect to $x$:
$\sqrt{3x+2} + \frac{1}{\sqrt{2x^2+4}}$

Find the derivative of the following function: $3 \cot x + 5 \operatorname{cosec} x$

Find the derivative of the following function (it is to be understood that $a, b, c, d, p, q, r$ and $s$ are fixed non-zero constants and $m$ and $n$ are integers): $\frac{\sin (x+a)}{\cos x}$

If $f(x)=|x-1|+|x-2|$, then $f^{\prime}(-2023)+f^{\prime}\left(\frac{2024}{2023}\right)+f^{\prime}(2023)=$

If $f(x) = \begin{cases} x-5, & \text{for } x \leq 1 \\ 4x^2-9, & \text{for } 1 < x < 2 \\ 3x+4, & \text{for } x \geq 2 \end{cases}$,then $f^{\prime}(2^{+})$ is equal to: