y=(4-9x)/(4+9x) SIMPLE PROBLEM

$Find the Derivative\mathit{ }of\mathit{:}\mathit{ }\mathit{y}\mathit{=}\frac{\mathit{4}\mathit{-}\mathit{9}\mathit{x}}{\mathit{4}\mathit{+}\mathit{9}\mathit{x}}$

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

$$\begin{gathered} \text{ \\ dydx=ddx4-9x4+9x \\ } \end{gathered}$$

$Step\mathit{ }\mathit{2}\mathit{:}\mathit{ }\mathit{A}\mathit{p}\mathit{p}\mathit{l}\mathit{y}\mathit{ }\mathit{t}\mathit{h}\mathit{e}\mathit{ }\mathit{Q}\mathit{u}\mathit{o}\mathit{t}\mathit{i}\mathit{e}\mathit{n}\mathit{t}\mathit{ }\mathit{R}\mathit{u}\mathit{l}\mathit{e}$

$$\begin{gathered} \text{ \\ ddxuv=vddx(u)-uddx(v)v2 \\ } \end{gathered}$$

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

$$\begin{gathered} \text{ \\ u=4-9x} \end{gathered}$$

$$\begin{gathered} \text{ \\ dudx=-9} \end{gathered}$$

$$\begin{gathered} \text{ \\ v=4+9x} \end{gathered}$$

$$\begin{gathered} \text{ \\ dvdx=9 \\ } \end{gathered}$$

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

$$\begin{gathered} \text{ \\ dydx=-9(4+9x)-9(4-9x)(4+9x)2 \\ } \end{gathered}$$

$\mathit{F}\mathit{i}\mathit{n}\mathit{a}\mathit{l}\mathbf{ }\mathit{A}\mathit{n}\mathit{s}\mathit{w}\mathit{e}\mathit{r}\mathbf{:}\mathbf{ }\mathbf{-}\frac{\mathbf{72}}{\mathbf{(}\mathbf{4}\mathbf{+}\mathbf{9}\mathit{x}{\mathbf{)}}^{\mathbf{2}}}$