What is (\partial)/(\partial y)(sqrt(4-x^2-y^2)) ?

The answer to (\partial)/(\partial y)(sqrt(4-x^2-y^2)) is -y/(sqrt(4-x^2-y^2))

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(\partial)/(\partial y)(sqrt(4-x^2-y^2))

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

- \frac{y}{4 - x ^{2} - y ^{2}}

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

= - \frac{y}{4 - x ^{2} - y ^{2}}

\int_{0}^{π} cos^{3} (2 x) d x

\int 1 + z d z

\int (x - 2)^{4} d x

\frac{d}{d x} ((5^{\frac{2}{3}} - x^{\frac{2}{3}})^{\frac{3}{2}})

\frac{d}{d x} (e (\frac{1}{x}))

What is (\partial)/(\partial y)(sqrt(4-x^2-y^2)) ?
The answer to (\partial)/(\partial y)(sqrt(4-x^2-y^2)) is -y/(sqrt(4-x^2-y^2))