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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

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