What is (\partial)/(\partial y)(sqrt(7-x^2-2y^2)) ?

The answer to (\partial)/(\partial y)(sqrt(7-x^2-2y^2)) is -(2y)/(sqrt(7-x^2-2y^2))

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(\partial)/(\partial y)(sqrt(7-x^2-2y^2))

\frac{\partial}{\partial y} (7 - x^{2} - 2 y^{2})

- \frac{2 y}{7 - x ^{2} - 2 y ^{2}}

Solution steps

\frac{\partial}{\partial y} (7 - x^{2} - 2 y^{2})

Treat

x

as a constant

Apply the chain rule:

\frac{1}{2 7 - x ^{2} - 2 y ^{2}} \frac{\partial}{\partial y} (7 - x^{2} - 2 y^{2})

= \frac{1}{2 7 - x ^{2} - 2 y ^{2}} \frac{\partial}{\partial y} (7 - x^{2} - 2 y^{2})

\frac{\partial}{\partial y} (7 - x^{2} - 2 y^{2}) = - 4 y

= \frac{1}{2 7 - x ^{2} - 2 y ^{2}} (- 4 y)

Simplify

\frac{1}{2 7 - x ^{2} - 2 y ^{2}} (- 4 y) : - \frac{2 y}{7 - x ^{2} - 2 y ^{2}}

= - \frac{2 y}{7 - x ^{2} - 2 y ^{2}}

\int \frac{x ^{5}}{( x ^{3} + 1 ) ( x ^{3} + 8 )} d x

\frac{( x ^{2} - 1 )}{x ^{2} + x + 1}

f (x) = x^{3}, at x = - 3

x \to - 2 lim (x - 2)

What is (\partial)/(\partial y)(sqrt(7-x^2-2y^2)) ?
The answer to (\partial)/(\partial y)(sqrt(7-x^2-2y^2)) is -(2y)/(sqrt(7-x^2-2y^2))