Find the derivative of $x^{5}(3-6x^{-9}).$

If $f(x) = \sum_{p=1}^7 p^2 \sin^{-1}\left(\frac{4}{5} \sin(px) - \frac{3}{5} \cos(px)\right)$, then the value of $\frac{df}{dx}$ at $x = 1$ is (Given that $\sin^{-1}(\sin x) = x$)

The derivative of $e^{3x} \sin 4x$ with respect to $x$ is:

Compute the derivative of $g(x) = \cot x$.

Differentiate the function with respect to $x$: $\sin^{3} x + \cos^{6} x$

If $y=(x-1)(x+2)(x^2+5)(x^4+8)$,then $\lim _{x \rightarrow-1}(\frac{d y}{d x})=$