What is (\partial)/(\partial x)(sqrt(12-x^2-y^2)) ?

The answer to (\partial)/(\partial x)(sqrt(12-x^2-y^2)) is -x/(sqrt(12-x^2-y^2))

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(\partial)/(\partial x)(sqrt(12-x^2-y^2))

\frac{\partial}{\partial x} (12 - x^{2} - y^{2})

- \frac{x}{12 - x ^{2} - y ^{2}}

Solution steps

\frac{\partial}{\partial x} (12 - x^{2} - y^{2})

Treat

y

as a constant

Apply the chain rule:

\frac{1}{2 12 - x ^{2} - y ^{2}} \frac{\partial}{\partial x} (12 - x^{2} - y^{2})

= \frac{1}{2 12 - x ^{2} - y ^{2}} \frac{\partial}{\partial x} (12 - x^{2} - y^{2})

\frac{\partial}{\partial x} (12 - x^{2} - y^{2}) = - 2 x

= \frac{1}{2 12 - x ^{2} - y ^{2}} (- 2 x)

Simplify

\frac{1}{2 12 - x ^{2} - y ^{2}} (- 2 x) : - \frac{x}{12 - x ^{2} - y ^{2}}

= - \frac{x}{12 - x ^{2} - y ^{2}}

y^{^{'}} = k y (100 - y)

\frac{d}{d x} (11 sin (x))

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

y = \frac{2 x}{x + 1}

7 (sin (t) y^{^{'}} + cos (t) y) = cos (t) sin^{3} (t)

What is (\partial)/(\partial x)(sqrt(12-x^2-y^2)) ?
The answer to (\partial)/(\partial x)(sqrt(12-x^2-y^2)) is -x/(sqrt(12-x^2-y^2))