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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (9 - 2 x^{2} - y^{2}) = - 4 x

= \frac{1}{2 9 - 2 x ^{2} - y ^{2}} (- 4 x)

Simplify

\frac{1}{2 9 - 2 x ^{2} - y ^{2}} (- 4 x) : - \frac{2 x}{9 - 2 x ^{2} - y ^{2}}

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

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