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

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

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

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

\frac{1}{2 x + y}

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

= \frac{1}{2 x + y} \cdot 1

Simplify

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

x, 100

\frac{d y}{d x} = x + 2 y, y (0) = 7

f (x) = 2 - 7 x^{2}, at x = 4

\frac{d}{d x} (e^{x} \cdot cos (y))

\int y e^{y} d y

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