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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

\frac{\partial}{\partial y} (4 - x^{2} - 4 y^{2}) = - 8 y

= \frac{1}{2 4 - x ^{2} - 4 y ^{2}} (- 8 y)

Simplify

\frac{1}{2 4 - x ^{2} - 4 y ^{2}} (- 8 y) : - \frac{4 y}{4 - x ^{2} - 4 y ^{2}}

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

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

\int \frac{8 + 7 x}{1 + x ^{2}} d x

t an g e n t f (x) = x^{2} - 2, at x = 0

\int \frac{2 x ^{3} - 4 x ^{2} + 18 x}{x ^{2} + 9} d x

\int x x x + 7 d x

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