Question

Differentiate " y=sin 2x (cos x)^2 " with respect to x: ​

Answer 1

Answer:

2 ( cos 2x ) ( cos x )²  -  ( sin 2x )²

Step-by-step explanation:

By the product rule

       $\frac{dy}{dx} = \frac{d}{dx}(\sin 2x)\times \cos^2x\ +\ \sin2x\times\frac{d}{dy}(\cos^2x)$

By the chain rule,

      $\frac{d}{dx}(\sin2x) = \cos2x\times\frac{d}{dx}(2x)=2\cos2x$

By the chain rule,

     $\frac{d}{dx}(\cos^2x) = 2\cos x\times\frac{d}{dx}(\cos x)=-2\cos x\sin x=-\sin 2x$

Putting these together gives

     $\frac{dy}{dx} = 2\cos2x\cos^2x - \sin^22x$

Answer 2

From the given

y=sin2 x+cos2 x

The right side of the equation is =1

y=1

dy/dx=d/dx(1)=0