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

The answer to (\partial)/(\partial y)(sqrt(y-x^2)) is 1/(2sqrt(y-x^2))

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

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

\frac{1}{2 y - x ^{2}}

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

= \frac{1}{2 y - x ^{2}} \cdot 1

Simplify

= \frac{1}{2 y - x ^{2}}

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What is (\partial)/(\partial y)(sqrt(y-x^2)) ?
The answer to (\partial)/(\partial y)(sqrt(y-x^2)) is 1/(2sqrt(y-x^2))