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

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

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

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

3 (x + y^{2})^{2}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (x + y^{2}) = 1

= 3 (x + y^{2})^{2} \cdot 1

Simplify

= 3 (x + y^{2})^{2}

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