What is (\partial)/(\partial x)(4x^{1/2}+y) ?

The answer to (\partial)/(\partial x)(4x^{1/2}+y) is 2/(x^{1/2)}

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(\partial)/(\partial x)(4x^{1/2}+y)

\frac{\partial}{\partial x} (4 x^{\frac{1}{2}} + y)

\frac{2}{x ^{\frac{1}{2}}}

Solution steps

\frac{\partial}{\partial x} (4 x^{\frac{1}{2}} + y)

Treat

y

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial x} (4 x^{\frac{1}{2}}) + \frac{\partial}{\partial x} (y)

\frac{\partial}{\partial x} (4 x^{\frac{1}{2}}) = \frac{2}{x ^{\frac{1}{2}}}

\frac{\partial}{\partial x} (y) = 0

= \frac{2}{x ^{\frac{1}{2}}} + 0

Simplify

= \frac{2}{x ^{\frac{1}{2}}}

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What is (\partial)/(\partial x)(4x^{1/2}+y) ?
The answer to (\partial)/(\partial x)(4x^{1/2}+y) is 2/(x^{1/2)}