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

The answer to (\partial)/(\partial y)(sqrt(4-x^2-2y)) is -1/(sqrt(4-x^2-2y))

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

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

- \frac{1}{4 - x ^{2} - 2 y}

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

What is (\partial)/(\partial y)(sqrt(4-x^2-2y)) ?
The answer to (\partial)/(\partial y)(sqrt(4-x^2-2y)) is -1/(sqrt(4-x^2-2y))