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

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

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

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

sin (2 x + 2 y)

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

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

Simplify

2 sin (x + y) cos (x + y) : sin (2 x + 2 y)

= sin (2 x + 2 y)

f (x) = 6 - x^{2}, g (x) = x

1 - 3 x

\int sin^{2} (r) d r

\int (6 csc (x) cot (x)) d x

x^{2} \cdot sin (x)

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