Tangent line to the given curves at the given point of tangency

$\mathit{y}\mathbf{=}{\mathit{x}}^{\mathbf{3}}\mathbf{(}\mathit{x}\mathbf{-}\mathbf{1}{\mathbf{)}}^{\mathbf{4}}\mathbf{ }\mathit{a}\mathit{t}\mathbf{ }\mathit{t}\mathit{h}\mathit{e}\mathbf{ }\mathit{p}\mathit{o}\mathit{i}\mathit{n}\mathit{t}\mathbf{ }\mathbf{(}\mathbf{2}\mathbf{,}\mathbf{ }\mathbf{8}\mathbf{)}$

$\mathbf{S}\mathbf{t}\mathbf{e}\mathbf{p}\mathbf{ }\mathbf{1}\mathbf{:}\mathbf{ }\mathbf{F}\mathbf{i}\mathbf{n}\mathbf{d}\mathbf{ }\mathbf{t}\mathbf{h}\mathbf{e}\mathbf{ }\mathbf{D}\mathbf{e}\mathbf{r}\mathbf{i}\mathbf{v}\mathbf{a}\mathbf{t}\mathbf{i}\mathbf{v}\mathbf{e}\mathbf{ }\mathbf{b}\mathbf{y}\mathbf{ }\mathbf{a}\mathbf{p}\mathbf{p}\mathbf{l}\mathbf{y}\mathbf{i}\mathbf{n}\mathbf{g}\mathbf{ }\mathbf{t}\mathbf{h}\mathbf{e}\mathbf{ }\mathbf{P}\mathbf{r}\mathbf{o}\mathbf{d}\mathbf{u}\mathbf{c}\mathbf{t}\mathbf{ }\mathbf{o}\mathbf{f}\mathbf{ }\mathbf{T}\mathbf{w}\mathbf{o}\mathbf{ }\mathbf{F}\mathbf{a}\mathbf{c}\mathbf{t}\mathbf{o}\mathbf{r}\mathbf{s}\mathbf{ }\mathbf{R}\mathbf{u}\mathbf{l}\mathbf{e}$

$$\begin{gathered} \text{ \\ ddx(uv)=udvdx+vdudx} \end{gathered}$$

$$\begin{gathered} \text{ \\ dudx=3x2} \end{gathered}$$

$$\begin{gathered} \text{ \\ dvdx=4(x-1)3} \end{gathered}$$

$$\begin{gathered} \text{ \\ ddxuv=4x3x-13+3x2x-14 \\ } \end{gathered}$$

$\mathbf{S}\mathbf{t}\mathbf{e}\mathbf{p}\mathbf{ }\mathbf{2}\mathbf{:}\mathbf{ }\mathbf{U}\mathbf{s}\mathbf{i}\mathbf{n}\mathbf{g}\mathbf{ }\mathbf{t}\mathbf{h}\mathbf{e}\mathbf{ }\mathbf{p}\mathbf{o}\mathbf{i}\mathbf{n}\mathbf{t}\mathbf{s}\mathbf{l}\mathbf{o}\mathbf{p}\mathbf{e}\mathbf{ }\mathbf{f}\mathbf{o}\mathbf{r}\mathbf{m}\mathbf{ }\mathbf{a}\mathbf{t}\mathbf{ }\mathbf{p}\mathbf{o}\mathbf{i}\mathbf{n}\mathbf{t}\mathbf{ }\mathbf{(}\mathbf{2}\mathbf{,}\mathbf{ }\mathbf{8}\mathbf{)}$

$$\begin{gathered} \text{ \\ y-8=44(x-2)} \end{gathered}$$

$$\begin{gathered} \text{ \\ y-8=44x-88} \end{gathered}$$

$$\begin{gathered} \text{ \\ y-44x-8+88=0} \end{gathered}$$

$$\begin{gathered} \text{ \\ y-44x+80=0} \end{gathered}$$

$$\begin{gathered} \text{ \\ 44x-y-80=0 \\ } \end{gathered}$$

$\mathbf{F}\mathbf{i}\mathbf{n}\mathbf{a}\mathbf{l}\mathbf{ }\mathbf{A}\mathbf{n}\mathbf{s}\mathbf{w}\mathbf{e}\mathbf{r}\mathbf{:}\mathbf{ }\mathbf{44}\mathit{x}\mathbf{-}\mathit{y}\mathbf{-}\mathbf{80}\mathbf{=}\mathbf{0}$