What is (\partial)/(\partial y)(sqrt(2x^2-4y^3)) ?

The answer to (\partial)/(\partial y)(sqrt(2x^2-4y^3)) is -(6y^2)/(sqrt(2x^2-4y^3))

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(\partial)/(\partial y)(sqrt(2x^2-4y^3))

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

- \frac{6 y ^{2}}{2 x ^{2} - 4 y ^{3}}

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

\frac{1}{2 2 x ^{2} - 4 y ^{3}} \frac{\partial}{\partial y} (2 x^{2} - 4 y^{3})

= \frac{1}{2 2 x ^{2} - 4 y ^{3}} \frac{\partial}{\partial y} (2 x^{2} - 4 y^{3})

\frac{\partial}{\partial y} (2 x^{2} - 4 y^{3}) = - 12 y^{2}

= \frac{1}{2 2 x ^{2} - 4 y ^{3}} (- 12 y^{2})

Simplify

\frac{1}{2 2 x ^{2} - 4 y ^{3}} (- 12 y^{2}) : - \frac{6 y ^{2}}{2 x ^{2} - 4 y ^{3}}

= - \frac{6 y ^{2}}{2 x ^{2} - 4 y ^{3}}

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What is (\partial)/(\partial y)(sqrt(2x^2-4y^3)) ?
The answer to (\partial)/(\partial y)(sqrt(2x^2-4y^3)) is -(6y^2)/(sqrt(2x^2-4y^3))