What is (\partial)/(\partial y)(sqrt(2x^2y-5y^2)) ?

The answer to (\partial)/(\partial y)(sqrt(2x^2y-5y^2)) is (x^2-5y)/(sqrt(2x^2y-5y^2))

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(\partial)/(\partial y)(sqrt(2x^2y-5y^2))

\frac{\partial}{\partial y} (2 x^{2} y - 5 y^{2})

\frac{x ^{2} - 5 y}{2 x ^{2} y - 5 y ^{2}}

Solution steps

\frac{\partial}{\partial y} (2 x^{2} y - 5 y^{2})

Treat

x

as a constant

Apply the chain rule:

\frac{1}{2 2 x ^{2} y - 5 y ^{2}} \frac{\partial}{\partial y} (2 x^{2} y - 5 y^{2})

= \frac{1}{2 2 x ^{2} y - 5 y ^{2}} \frac{\partial}{\partial y} (2 x^{2} y - 5 y^{2})

\frac{\partial}{\partial y} (2 x^{2} y - 5 y^{2}) = 2 x^{2} - 10 y

= \frac{1}{2 2 x ^{2} y - 5 y ^{2}} (2 x^{2} - 10 y)

Simplify

\frac{1}{2 2 x ^{2} y - 5 y ^{2}} (2 x^{2} - 10 y) : \frac{x ^{2} - 5 y}{2 x ^{2} y - 5 y ^{2}}

= \frac{x ^{2} - 5 y}{2 x ^{2} y - 5 y ^{2}}

What is (\partial)/(\partial y)(sqrt(2x^2y-5y^2)) ?
The answer to (\partial)/(\partial y)(sqrt(2x^2y-5y^2)) is (x^2-5y)/(sqrt(2x^2y-5y^2))