What is the derivative of sin(2x)cos(2x)?

2 Answers
Harish Chandra Rajpoot
Jul 21, 2018

2\cos(4x)

Explanation:

Given function:

\sin (2x)\cos (2x)

1/2(2\sin (2x)\cos (2x))

1/2\sin (4x)

Differentiating given function w.r.t. x as follows

d/dx(1/2\sin(4x))

=1/2\d/dx(\sin(4x))

=1/2\cos(4x)d/dx(4x)

=1/2\cos(4x)(4)

=2\cos(4x)

Jim G.
Jul 21, 2018

2cos4x

Explanation:

"differentiate using the "color(blue)"product/chain rule"

"given "y=f(x)g(x)" then"

dy/dx=f(x)g'(x)+g(x)f'(x)larrcolor(blue)"product rule"

f(x)=sin2xrArrf'(x)=2cos2x

g(x)=cos2xrArrg'(x)=-2sin2x

d/dx(sin2xcos2x)

=-2sin^2 2x+2cos^2 2x

=2(cos^2 2x-sin^2 2x)=2cos4x

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