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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int (3 x - x^{- 1})^{2} d x

\frac{d}{d x} (\frac{x}{x ^{2} + a ^{2}})

\int \frac{1}{e ^{3 y}} d y

f (r) = 2 π r^{2}

\frac{d}{d x} ((8 x + 7) (x^{2} - 3 x))

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