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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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\int \frac{( x ^{2} - 49 )}{x ^{3}} d x

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