Power of x Rule in Finding the Derivative

$\mathit{F}\mathit{i}\mathit{n}\mathit{d}\mathbf{ }\mathit{t}\mathit{h}\mathit{e}\mathbf{ }\mathit{D}\mathit{e}\mathit{r}\mathit{i}\mathit{v}\mathit{a}\mathit{t}\mathit{i}\mathit{v}\mathit{e}\mathbf{ }\mathit{o}\mathit{f}\mathbf{:} \mathit{y}\mathbf{=}\left({\mathit{x}}^{\mathbf{3}}\mathbf{-}\mathbf{6}\mathit{x}\right)\left(\mathbf{2}\mathbf{-}\mathbf{4}{\mathit{x}}^{\mathbf{3}}\right)$

$\mathit{S}\mathit{t}\mathit{e}\mathit{p}\mathit{ }\mathit{1}\mathit{:}\mathit{ }\mathit{S}\mathit{i}\mathit{m}\mathit{p}\mathit{l}\mathit{i}\mathit{f}\mathit{y}$

$$\begin{gathered} \text{ \\ y=2x3-4x6--24x4-12x \\ } \end{gathered}$$

$\mathit{S}\mathit{t}\mathit{e}\mathit{p}\mathbf{ }\mathbf{2}\mathbf{:}\mathbf{ }\mathit{M}\mathit{u}\mathit{l}\mathit{t}\mathit{i}\mathit{p}\mathit{l}\mathit{y}\mathbf{ }\mathit{b}\mathit{o}\mathit{t}\mathit{h}\mathbf{ }\mathit{s}\mathit{i}\mathit{d}\mathit{e}\mathbf{ }\mathit{b}\mathit{y}\mathbf{ }\frac{\mathit{d}}{\mathit{d}\mathit{x}}$

$$\begin{gathered} \text{ \\ dydx=ddx2x3-4x6--24x4-12x \\ } \end{gathered}$$

$\mathit{S}\mathit{t}\mathit{e}\mathit{p}\mathbf{ 3}\mathbf{:}\mathbf{ }\mathit{A}\mathit{p}\mathit{p}\mathit{l}\mathit{y}\mathbf{ }\mathit{t}\mathit{h}\mathit{e} \mathit{P}\mathit{o}\mathit{w}\mathit{e}\mathit{r}\mathit{o}\mathit{f}\mathbf{ }\mathit{x}\mathbf{ }\mathit{R}\mathit{u}\mathit{l}\mathit{e} \mathit{i}\mathit{n}\mathbf{ }\frac{\mathbf{d}}{\mathbf{dx}}\left(\mathbf{2}{\mathbf{x}}^{\mathbf{3}}\mathbf{-}\mathbf{4}{\mathbf{x}}^{\mathbf{6}}\mathbf{-}\mathbf{24}{\mathbf{x}}^{\mathbf{4}}\mathbf{-}\mathbf{12}\mathbf{x}\right)$

$$\begin{gathered} \text{ \\ ddxcxn=cnxn-1 \\ } \end{gathered}$$

$\mathbf{S}\mathbf{o}\mathbf{l}\mathbf{u}\mathbf{t}\mathbf{i}\mathbf{o}\mathbf{n}\mathbf{:}$

$$\begin{gathered} \text{ \\ dydx=6x2-24x5-96x3-12 \\ } \end{gathered}$$

$\mathbf{S}\mathbf{i}\mathbf{m}\mathbf{p}\mathbf{l}\mathbf{i}\mathbf{f}\mathbf{y}\mathbf{:}\mathbf{ }6(-4{\mathrm{x}}^5-16{\mathrm{x}}^3+{\mathrm{x}}^2-2)$

$\mathit{F}\mathit{i}\mathit{n}\mathit{a}\mathit{l}\mathbf{ }\mathit{A}\mathit{n}\mathit{s}\mathit{w}\mathit{e}\mathit{r}\mathbf{:}\mathbf{ }\mathbf{6}\left(\mathbf{-}\mathbf{4}{\mathbf{x}}^{\mathbf{5}}\mathbf{-}\mathbf{16}{\mathbf{x}}^{\mathbf{3}}\mathbf{+}{\mathbf{x}}^{\mathbf{2}}\mathbf{-}\mathbf{2}\right)$