Answer:
The function is given below as
[tex]\mleft(\sqrt{1-e^{-x}}\mright)\mleft(e^{-x}+1\mright)^2[/tex]
By applying the product rule,
[tex]\quad \mleft(f\cdot g\mright)^{\prime}=f\: ^{\prime}\cdot g+f\cdot g[/tex][tex]\frac{d}{dx}\mleft(\sqrt{1-e^{-x}}\mright)\mleft(e^{-x}+1\mright)^2+\frac{d}{dx}\mleft(\mleft(e^{-x}+1\mright)^2\mright)\sqrt{1-e^{-x}}[/tex]
