Calculating for derivative using General Power Rule

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

$\mathit{}\mathit{S}\mathit{t}\mathit{e}\mathit{p}\mathbf{ }\mathbf{1}\mathbf{:}\mathbf{ }\mathit{M}\mathit{u}\mathit{l}\mathit{t}\mathit{i}\mathit{p}\mathit{l}\mathit{y}\mathbf{ }\mathit{b}\mathit{o}\mathit{t}\mathit{h}\mathbf{ }\mathit{s}\mathit{i}\mathit{d}\mathit{e}\mathbf{ }\mathit{b}\mathit{y}\mathbf{ }\frac{\mathit{d}}{\mathit{d}\mathit{x}}$

$$\begin{gathered} \text{ \\ dydx=ddx3x4-2x2+42 \\ } \end{gathered}$$

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

$$\begin{gathered} \text{ \\ ddxcun=cnun-1dudx \\ } \end{gathered}$$

$\mathbf{G}\mathbf{i}\mathbf{v}\mathbf{e}\mathbf{n}\mathbf{:}$

$$\begin{gathered} \text{ \\ u=3x4-2x2+4} \end{gathered}$$

$$\begin{gathered} \text{ \\ dudx=12x3-4x} \end{gathered}$$

$$\begin{gathered} \text{ \\ n=2} \end{gathered}$$

$$\begin{gathered} \text{ \\ c=1 \\ } \end{gathered}$$

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

$$\begin{gathered} \text{ \\ dydx=23x4-2x2+42-112x3-4x} \end{gathered}$$

$$\begin{gathered} \text{ \\ dydx=24x3-8x3x4-2x2+42-1 \\ } \end{gathered}$$

$\mathit{F}\mathit{i}\mathit{n}\mathit{a}\mathit{l}\mathbf{ }\mathit{A}\mathit{n}\mathit{s}\mathit{w}\mathit{e}\mathit{r}\mathbf{:}\mathbf{ }\mathbf{24}{\mathbf{x}}^{\mathbf{3}}\mathbf{-}\mathbf{8}\mathbf{x}{\left(\mathbf{3}{\mathit{x}}^{\mathbf{4}}\mathbf{-}\mathbf{2}{\mathit{x}}^{\mathbf{2}}\mathbf{+}\mathbf{4}\right)}^{\mathbf{2}\mathbf{-}\mathbf{1}}$