[tex]\\ \sf\longmapsto \dfrac{d}{dx}2xe^x[/tex]
[tex]\\ \sf\longmapsto \dfrac{d}{dx}2x(e^x)[/tex]
[tex]\\ \sf\longmapsto 2x\dfrac{d}{dx}e^x+e^x\dfrac{d}{dx}2x[/tex]
[tex]\\ \sf\longmapsto 2xe^x+2e^x[/tex]
[tex]\\ \sf\longmapsto 2e^x(x+1)[/tex]
Answer:
[tex]{ \tt{y = 2 {xe}^{x} }}[/tex]
» We are going to use product rule of ∂
[tex]{ \boxed{ \tt{ \: \frac{dy}{dx} = { \huge{ \red{v}}} \frac{du}{dx} } + { \huge{ \green{u}}} \frac{dv}{dx} }}[/tex]
[tex]{ \tt{ \frac{dy}{dx} = ( {e}^{x} )(2) + (2x)( {e}^{x} )}} \\ \\ { \tt{ \frac{dy}{dx} = 2 {e}^{x} + 2x {e}^{x} }} \\ \\ { \boxed{ \rm{ \: \frac{dy}{dx} = 2 {e}^{x}(1 + x) }}}[/tex]
