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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int_{0}^{8} \frac{5}{x ^{\frac{2}{3}}} d x

y = 2 x^{2} + 1

\frac{d}{d x} ((cos (3 x))^{x})

f (x) = sin (x) ln (x^{2} + 1)

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