What is (\partial)/(\partial x)(sqrt(x+2y)) ?

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

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(\partial)/(\partial x)(sqrt(x+2y))

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

\int \frac{5 x + 4}{( x + 8 ) ^{2} ( x - 1 )} d x

\frac{s ^{2} + 9}{s ( s + 4 )}

\frac{d y}{d x} = \frac{x - 1}{x + 3} \frac{y - 2}{y - 3}

\frac{2 s + 3}{s ^{2} + 6 s + 13}

\frac{x}{x - 2}

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