What is (\partial)/(\partial x)(sqrt(4x+2y)) ?

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

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(\partial)/(\partial x)(sqrt(4x+2y))

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

\frac{2}{4 x + 2 y}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

= \frac{1}{2 4 x + 2 y} \cdot 4

Simplify

\frac{1}{2 4 x + 2 y} \cdot 4 : \frac{2}{4 x + 2 y}

= \frac{2}{4 x + 2 y}

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