What is (\partial)/(\partial y)(sqrt(25-x^2-5y)) ?

The answer to (\partial)/(\partial y)(sqrt(25-x^2-5y)) is -5/(2sqrt(25-x^2-5y))

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(\partial)/(\partial y)(sqrt(25-x^2-5y))

\frac{\partial}{\partial y} (25 - x^{2} - 5 y)

- \frac{5}{2 25 - x ^{2} - 5 y}

Solution steps

\frac{\partial}{\partial y} (25 - x^{2} - 5 y)

Treat

x

as a constant

Apply the chain rule:

\frac{1}{2 25 - x ^{2} - 5 y} \frac{\partial}{\partial y} (25 - x^{2} - 5 y)

= \frac{1}{2 25 - x ^{2} - 5 y} \frac{\partial}{\partial y} (25 - x^{2} - 5 y)

\frac{\partial}{\partial y} (25 - x^{2} - 5 y) = - 5

= \frac{1}{2 25 - x ^{2} - 5 y} (- 5)

Simplify

\frac{1}{2 25 - x ^{2} - 5 y} (- 5) : - \frac{5}{2 25 - x ^{2} - 5 y}

= - \frac{5}{2 25 - x ^{2} - 5 y}

\int 6 x 1 + x^{2} d x

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\int π t - t^{2} cos (n t) d t

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What is (\partial)/(\partial y)(sqrt(25-x^2-5y)) ?
The answer to (\partial)/(\partial y)(sqrt(25-x^2-5y)) is -5/(2sqrt(25-x^2-5y))