Function Rule in Finding the DERIVATIVE

$\mathit{F}\mathit{i}\mathit{n}\mathit{d}\mathbf{ }\mathit{t}\mathit{h}\mathit{e}\mathbf{ }\mathit{D}\mathit{e}\mathit{r}\mathit{i}\mathit{v}\mathit{a}\mathit{t}\mathit{i}\mathit{v}\mathit{e}\mathbf{ }\mathit{o}\mathit{f}\mathbf{:} \mathit{y}\mathbf{=}\sqrt{\mathbf{3}\mathit{x}}\mathbf{-}\frac{\mathbf{1}}{\sqrt[\mathbf{3}]{\mathbf{5}\mathit{x}}}$

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

$$\begin{gathered} \text{ \\ dydx=ddx3x-ddx15x3 \\ } \end{gathered}$$

$\mathit{S}\mathit{t}\mathit{e}\mathit{p}\mathbf{ }\mathbf{2}\mathbf{:}\mathbf{ }\mathit{A}\mathit{p}\mathit{p}\mathit{l}\mathit{y}\mathbf{ }\mathit{t}\mathit{h}\mathit{e}\mathbf{ }\mathit{S}\mathit{q}\mathit{u}\mathit{a}\mathit{r}\mathit{e}\mathbf{ }\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathbf{ }\mathit{o}\mathit{f}\mathbf{ }\mathit{a}\mathbf{ }\mathit{F}\mathit{u}\mathit{n}\mathit{c}\mathit{t}\mathit{i}\mathit{o}\mathit{n}\mathbf{ }\mathit{R}\mathit{u}\mathit{l}\mathit{e} \mathit{i}\mathit{n}\mathbf{ }\frac{\mathbf{d}}{\mathbf{dx}}\sqrt{\mathbf{3}\mathit{x}}$

$$\begin{gathered} \text{ \\ ddxu=12uddx(u)} \end{gathered}$$

$$\begin{gathered} \text{ \\ ddx3x=323x simplify = 32x \\ } \end{gathered}$$

$\mathit{S}\mathit{t}\mathit{e}\mathit{p}\mathbf{ }\mathbf{3}\mathbf{:}\mathbf{ }\mathit{A}\mathit{p}\mathit{p}\mathit{l}\mathit{y}\mathbf{ }\mathit{t}\mathit{h}\mathit{e}\mathbf{ }\mathit{Q}\mathit{u}\mathit{o}\mathit{t}\mathit{i}\mathit{e}\mathit{n}\mathit{t}\mathbf{ }\mathit{R}\mathit{u}\mathit{l}\mathit{e}\mathbf{ }\mathit{i}\mathit{n}\mathbf{ }\mathbf{-}\frac{\mathbf{d}}{\mathbf{d}\mathbf{x}}\frac{\mathbf{1}}{\sqrt[\mathbf{3}]{\mathbf{5}\mathit{x}}}$

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

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

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

$$\begin{gathered} \text{ \\ dudx=0} \end{gathered}$$

$$\begin{gathered} \text{ \\ v=5x3} \end{gathered}$$

$$\begin{gathered} \text{ \\ dvdx=533x23} \end{gathered}$$

$\mathit{F}\mathit{i}\mathit{n}\mathit{a}\mathit{l}\mathbf{ }\mathit{A}\mathit{n}\mathit{s}\mathit{w}\mathit{e}\mathit{r}\mathbf{:}\mathbf{ }\frac{\sqrt{\mathbf{3}}}{\mathbf{2}\sqrt{\mathit{x}}}\mathbf{-}\frac{\mathbf{1}}{\mathbf{3}\sqrt[\mathbf{3}]{\mathbf{5}}{\mathit{x}}^{\frac{\mathbf{4}}{\mathbf{3}}}}$