How do you find the derivative of y=cos(2x) ?
Solve for differentiation
Given: dydx=ddx(cos(2x))We know that ddx(cos(x))=-sin(x)
Applying chain rule df(g(x))dx=dd(g(x))f(g(x))×ddxg(x)
Here g(x)=2x and f(g(x))=cos(2x)
ddx(cos(2x))=dd(2x)(cos(2x))×ddx(2x)
⇒dydx=(-sin(2x))ddx(2x)
⇒dydx=(-sin(2x))2⇒dydx=-2sin(2x)
Hence, the derivative of y=cos(2x) is dydx=-2sin2x.