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

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

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

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

\frac{1}{2 x}

Solution steps

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

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)

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

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

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

Simplify

= \frac{1}{2 x}

f (x) = - x^{3} + 4 x - 2, at x = - 2

\frac{1}{1 - 4 x}

\int sin^{5} (x co) s^{3} x d x

f (x) = - 3 x^{\frac{3}{2}}, at x = 4

\frac{\partial}{\partial x} (x y e^{x})

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