Answer:
[tex]\frac{dy}{dx} = 2x ( 2cos2x) +sin2x[/tex]
[tex]\frac{dy}{dx} = 4x( cos2x)+sin2x[/tex]
Step-by-step explanation:
Given y = x sin2x .....(1)
Applying UV formula [tex]\frac{d(UV)}{dx} = u \frac{dv}{dx} + v\frac{du}{dx}[/tex]
Differentiating with respective to 'x' we get
[tex]\frac{dy}{dx} = x ( 2cos2x)\frac{d(2x)}{dx} +sin2x (1)[/tex]
[tex]\frac{dy}{dx} = x ( 2cos2x)(2) +sin2x (1)[/tex]
Final answer:-
[tex]\frac{dy}{dx} = 4x( cos2x)+sin2x[/tex]