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

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

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

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

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

Use the Double Angle identity:

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

= sin (2 (x - y))

y = 2 + 5 x^{2} - 2 x^{3}

\int (3 x - 16)^{7} d x

\int_{1}^{2} e^{l n (x)} d x

x y^{^{'}} = (1 - y^{2})^{\frac{1}{2}}

y = \frac{x + 1}{x ^{3} + x - 2}

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