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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d}{d x} (ln (\frac{x ^{2}}{2 x ^{2} + 3 x + 2}))

y = \frac{π}{( 2 x ) ^{4}}

\int \frac{2}{x ^{2} + 9} d x

\frac{x d y}{d x} = 2 y

\frac{d y}{d x}, y = 2 9^{x}

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