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

The answer to (\partial)/(\partial y)(sin^2(xy)) is xsin(2xy)

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

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

x sin (2 x 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) x

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

Use the Double Angle identity:

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

= x sin (2 x y)

y^{^{'}} + \frac{4 y}{x} = - \frac{3}{x}, y (1) = - 2

\int - 2 cos (\frac{x}{2}) d x

x \to 2 lim (x^{2} + 3 x)

\int 9 x^{- 2} d x

\frac{d}{d x} (\frac{x - 2}{x + 2})

What is (\partial)/(\partial y)(sin^2(xy)) ?
The answer to (\partial)/(\partial y)(sin^2(xy)) is xsin(2xy)