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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= 0 - (- \frac{x}{y - x ^{2}})

Simplify

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

cos (\frac{x}{2})

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