What is (\partial)/(\partial x)(sqrt(9-x^2-3y)) ?

The answer to (\partial)/(\partial x)(sqrt(9-x^2-3y)) is -x/(sqrt(9-x^2-3y))

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(\partial)/(\partial x)(sqrt(9-x^2-3y))

\frac{\partial}{\partial x} (9 - x^{2} - 3 y)

- \frac{x}{9 - x ^{2} - 3 y}

Solution steps

\frac{\partial}{\partial x} (9 - x^{2} - 3 y)

Treat

y

as a constant

Apply the chain rule:

\frac{1}{2 9 - x ^{2} - 3 y} \frac{\partial}{\partial x} (9 - x^{2} - 3 y)

= \frac{1}{2 9 - x ^{2} - 3 y} \frac{\partial}{\partial x} (9 - x^{2} - 3 y)

\frac{\partial}{\partial x} (9 - x^{2} - 3 y) = - 2 x

= \frac{1}{2 9 - x ^{2} - 3 y} (- 2 x)

Simplify

\frac{1}{2 9 - x ^{2} - 3 y} (- 2 x) : - \frac{x}{9 - x ^{2} - 3 y}

= - \frac{x}{9 - x ^{2} - 3 y}

What is (\partial)/(\partial x)(sqrt(9-x^2-3y)) ?
The answer to (\partial)/(\partial x)(sqrt(9-x^2-3y)) is -x/(sqrt(9-x^2-3y))