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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

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