What is (\partial)/(\partial y)(5sqrt(x^2+y^2)) ?

The answer to (\partial)/(\partial y)(5sqrt(x^2+y^2)) is (5y)/(sqrt(x^2+y^2))

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(\partial)/(\partial y)(5sqrt(x^2+y^2))

\frac{\partial}{\partial y} (5 x^{2} + y^{2})

\frac{5 y}{x ^{2} + y ^{2}}

Solution steps

\frac{\partial}{\partial y} (5 x^{2} + y^{2})

Treat

x

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 5 \frac{\partial}{\partial y} (x^{2} + y^{2})

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

= 5 \cdot \frac{1}{2 x ^{2} + y ^{2}} \cdot 2 y

Simplify

5 \cdot \frac{1}{2 x ^{2} + y ^{2}} \cdot 2 y : \frac{5 y}{x ^{2} + y ^{2}}

= \frac{5 y}{x ^{2} + y ^{2}}

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What is (\partial)/(\partial y)(5sqrt(x^2+y^2)) ?
The answer to (\partial)/(\partial y)(5sqrt(x^2+y^2)) is (5y)/(sqrt(x^2+y^2))