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

The answer to (\partial)/(\partial x)(sin^2(xy)) is ysin(2xy)

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

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

y sin (2 x y)

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Use the Double Angle identity:

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

= y sin (2 x y)

What is (\partial)/(\partial x)(sin^2(xy)) ?
The answer to (\partial)/(\partial x)(sin^2(xy)) is ysin(2xy)