Find the derivative

$\mathrm{Find} \mathrm{the} \mathrm{derivative} \mathrm{of}: \mathrm{y}=2({\mathrm{x}}^3-2\mathrm{x}+5{)}^4$

$\mathrm{Step} 1: \mathrm{Multiply} \mathrm{both} \mathrm{side} \mathrm{by} \frac{\mathrm{d}}{\mathrm{dx}}$
$\frac{dy}{dx}=\frac{d}{dx}2{\left({\mathrm{x}}^3-2\mathrm{x}+5\right)}^4$

$\mathrm{Remember}:$
$\left(1\right) \frac{\mathrm{d}}{\mathrm{dx}}\left({\mathrm{cu}}^{\mathrm{n}}\right)={\mathrm{cnu}}^{\mathrm{n}-1}\frac{\mathrm{du}}{\mathrm{dx}}$

$\mathrm{Given}:$

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

$$\begin{gathered} \text{ \\ n = 4 } \end{gathered}$$

$$\begin{gathered} \text{ \\ u = x3-2x+5} \end{gathered}$$

$$\begin{gathered} \text{ \\ dudx=3x2-2 \\ } \end{gathered}$$

$\mathrm{Solution}:$

$$\begin{gathered} \text{ \\ dydx=(2)(4)x3-2x+54-13x2-2 \\ } \end{gathered}$$

$\mathrm{Final} \mathrm{Answer}: 24{\mathrm{x}}^2-16({\mathrm{x}}^3-2\mathrm{x}+5{)}^3$