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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

y^{^{''}} + 4 y = 16 sec (2 t)

\frac{d}{d t} (4 t^{3})

\int_{0}^{\frac{π}{2}} cos^{5} (x) d x

2 x^{4} + \frac{3 x}{5}, at x = 0

\int (2 + 2 x) e^{(4 x + 2 x^{2})} d x

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