What is (\partial)/(\partial x)(sqrt(x)+sqrt(y+4)) ?

The answer to (\partial)/(\partial x)(sqrt(x)+sqrt(y+4)) is 1/(2sqrt(x))

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(\partial)/(\partial x)(sqrt(x)+sqrt(y+4))

\frac{\partial}{\partial x} (x + y + 4)

\frac{1}{2 x}

Solution steps

\frac{\partial}{\partial x} (x + y + 4)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial x} (y + 4) = 0

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

Simplify

= \frac{1}{2 x}

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