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

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

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

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

cos (x^{2} y) x^{2}

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

= cos (x^{2} y) \frac{\partial}{\partial y} (x^{2} y)

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

= cos (x^{2} y) x^{2}

\frac{d}{d x} ((x^{3} + 6 x)^{4})

\frac{2 e ^{- 2 s}}{3 s ^{2} + 12}

3 y^{^{'}} + y = 6 t, y (0) = 3

\frac{d}{d x} (6 x + 5)

\frac{d y}{d x} = 4 x^{3}

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