What is (\partial)/(\partial x)(2+sqrt(y-x^2+9)) ?

The answer to (\partial)/(\partial x)(2+sqrt(y-x^2+9)) is -x/(sqrt(y+9-x^2))

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(\partial)/(\partial x)(2+sqrt(y-x^2+9))

\frac{\partial}{\partial x} (2 + y - x^{2} + 9)

- \frac{x}{y + 9 - x ^{2}}

Solution steps

\frac{\partial}{\partial x} (2 + y - x^{2} + 9)

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} + 9)

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

\frac{\partial}{\partial x} (y - x^{2} + 9) = - \frac{x}{y - x ^{2} + 9}

= 0 - \frac{x}{y - x ^{2} + 9}

Simplify

= - \frac{x}{y + 9 - x ^{2}}

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What is (\partial)/(\partial x)(2+sqrt(y-x^2+9)) ?
The answer to (\partial)/(\partial x)(2+sqrt(y-x^2+9)) is -x/(sqrt(y+9-x^2))