What is (\partial)/(\partial y)(sqrt(16-x^2-4y)) ?

The answer to (\partial)/(\partial y)(sqrt(16-x^2-4y)) is -2/(sqrt(16-x^2-4y))

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(\partial)/(\partial y)(sqrt(16-x^2-4y))

\frac{\partial}{\partial y} (16 - x^{2} - 4 y)

- \frac{2}{16 - x ^{2} - 4 y}

Solution steps

\frac{\partial}{\partial y} (16 - x^{2} - 4 y)

Treat

x

as a constant

Apply the chain rule:

\frac{1}{2 16 - x ^{2} - 4 y} \frac{\partial}{\partial y} (16 - x^{2} - 4 y)

= \frac{1}{2 16 - x ^{2} - 4 y} \frac{\partial}{\partial y} (16 - x^{2} - 4 y)

\frac{\partial}{\partial y} (16 - x^{2} - 4 y) = - 4

= \frac{1}{2 16 - x ^{2} - 4 y} (- 4)

Simplify

\frac{1}{2 16 - x ^{2} - 4 y} (- 4) : - \frac{2}{16 - x ^{2} - 4 y}

= - \frac{2}{16 - x ^{2} - 4 y}

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What is (\partial)/(\partial y)(sqrt(16-x^2-4y)) ?
The answer to (\partial)/(\partial y)(sqrt(16-x^2-4y)) is -2/(sqrt(16-x^2-4y))