What is (\partial)/(\partial x)(sin^2(ax)) ?

The answer to (\partial)/(\partial x)(sin^2(ax)) is asin(2ax)

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(\partial)/(\partial x)(sin^2(ax))

\frac{\partial}{\partial x} (sin^{2} (a x))

a sin (2 a x)

Solution steps

\frac{\partial}{\partial x} (sin^{2} (a x))

Apply the chain rule:

2 sin (a x) \frac{\partial}{\partial x} (sin (a x))

= 2 sin (a x) \frac{\partial}{\partial x} (sin (a x))

\frac{\partial}{\partial x} (sin (a x)) = cos (a x) a

= 2 sin (a x) cos (a x) a

Use the Double Angle identity:

2 sin (x) cos (x) = sin (2 x)

= a sin (2 a x)

What is (\partial)/(\partial x)(sin^2(ax)) ?
The answer to (\partial)/(\partial x)(sin^2(ax)) is asin(2ax)