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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

= 3 (sin (x^{2} y))^{2} cos (x^{2} y) x^{2}

Simplify

= 3 x^{2} sin^{2} (x^{2} y) cos (x^{2} y)

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

y = e^{- \frac{1}{2} x}

(2 x^{3} + 5 x) (x - 3) (x + 2)

\frac{d}{d x} (ln (y - x))

- x^{2} + 8 x - 9, (\frac{1}{2} x) + 1, x = 3, x = 5

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