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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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