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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{\partial}{\partial y} (2) = 0

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

= 0 - \frac{1}{2 y - x ^{2}}

Simplify

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

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