What is (\partial)/(\partial y)((x^2+y^2)^{1/2}) ?

The answer to (\partial)/(\partial y)((x^2+y^2)^{1/2}) is y/((x^2+y^2)^{1/2)}

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

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

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

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

Simplify

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

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

f (x) = x^{2} - 4

\int \frac{1}{x ^{2} ( x + 1 ) ^{2}} d x

x - 2

7 x - 4 x

y^{^{'}} - y^{\frac{5}{3}} = 0

What is (\partial)/(\partial y)((x^2+y^2)^{1/2}) ?
The answer to (\partial)/(\partial y)((x^2+y^2)^{1/2}) is y/((x^2+y^2)^{1/2)}