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

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

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(\partial)/(\partial y)(sqrt(x^2+2y^2))

\frac{\partial}{\partial y} (x^{2} + 2 y^{2})

\frac{2 y}{x ^{2} + 2 y ^{2}}

Solution steps

\frac{\partial}{\partial y} (x^{2} + 2 y^{2})

Treat

x

as a constant

Apply the chain rule:

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

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

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

= \frac{1}{2 x ^{2} + 2 y ^{2}} \cdot 4 y

Simplify

\frac{1}{2 x ^{2} + 2 y ^{2}} \cdot 4 y : \frac{2 y}{x ^{2} + 2 y ^{2}}

= \frac{2 y}{x ^{2} + 2 y ^{2}}

\frac{d y}{d x} = 4 x - y

\int \frac{x ^{2} - 3 x + 1}{x + 1} d x

\frac{\partial}{\partial y} (3 x e^{- 2 x y})

(\frac{d y}{d x}) = y - y

\int \frac{1}{x ^{2} + 4 x + 8} d x

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