What is (\partial)/(\partial x)(sin^2(x-3y)) ?

The answer to (\partial)/(\partial x)(sin^2(x-3y)) is sin(2(x-3y))

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(\partial)/(\partial x)(sin^2(x-3y))

\frac{\partial}{\partial x} (sin^{2} (x - 3 y))

sin (2 (x - 3 y))

Solution steps

\frac{\partial}{\partial x} (sin^{2} (x - 3 y))

Treat

y

as a constant

Apply the chain rule:

2 sin (x - 3 y) \frac{\partial}{\partial x} (sin (x - 3 y))

= 2 sin (x - 3 y) \frac{\partial}{\partial x} (sin (x - 3 y))

\frac{\partial}{\partial x} (sin (x - 3 y)) = cos (x - 3 y)

= 2 sin (x - 3 y) cos (x - 3 y)

Use the Double Angle identity:

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

= sin (2 (x - 3 y))

arctan (u)

\int_{0}^{π} sin^{2} (x) d x

\frac{d}{d x} (2 x^{2} + 3 x - 1)

\int 7 x^{- 3} d x

f (x) = x^{1}

What is (\partial)/(\partial x)(sin^2(x-3y)) ?
The answer to (\partial)/(\partial x)(sin^2(x-3y)) is sin(2(x-3y))