What is (\partial)/(\partial x)((1+2xy^2)^3) ?

The answer to (\partial)/(\partial x)((1+2xy^2)^3) is 6y^2(1+2xy^2)^2

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(\partial)/(\partial x)((1+2xy^2)^3)

\frac{\partial}{\partial x} ((1 + 2 x y^{2})^{3})

6 y^{2} (1 + 2 x y^{2})^{2}

Solution steps

\frac{\partial}{\partial x} ((1 + 2 x y^{2})^{3})

Treat

y

as a constant

Apply the chain rule:

3 (1 + 2 x y^{2})^{2} \frac{\partial}{\partial x} (1 + 2 x y^{2})

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

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

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

Simplify

= 6 y^{2} (1 + 2 x y^{2})^{2}

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What is (\partial)/(\partial x)((1+2xy^2)^3) ?
The answer to (\partial)/(\partial x)((1+2xy^2)^3) is 6y^2(1+2xy^2)^2