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

The answer to (\partial)/(\partial y)((x^3+2y^2)^3) is 12y(x^3+2y^2)^2

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

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

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

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

\frac{\partial}{\partial y} (x^{3} + 2 y^{2}) = 4 y

= 3 (x^{3} + 2 y^{2})^{2} \cdot 4 y

Simplify

= 12 y (x^{3} + 2 y^{2})^{2}

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What is (\partial)/(\partial y)((x^3+2y^2)^3) ?
The answer to (\partial)/(\partial y)((x^3+2y^2)^3) is 12y(x^3+2y^2)^2