What is (\partial)/(\partial x)(sqrt(3x+4y)) ?

The answer to (\partial)/(\partial x)(sqrt(3x+4y)) is 3/(2sqrt(3x+4y))

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(\partial)/(\partial x)(sqrt(3x+4y))

\frac{\partial}{\partial x} (3 x + 4 y)

\frac{3}{2 3 x + 4 y}

Solution steps

\frac{\partial}{\partial x} (3 x + 4 y)

Treat

y

as a constant

Apply the chain rule:

\frac{1}{2 3 x + 4 y} \frac{\partial}{\partial x} (3 x + 4 y)

= \frac{1}{2 3 x + 4 y} \frac{\partial}{\partial x} (3 x + 4 y)

\frac{\partial}{\partial x} (3 x + 4 y) = 3

= \frac{1}{2 3 x + 4 y} \cdot 3

Simplify

\frac{1}{2 3 x + 4 y} \cdot 3 : \frac{3}{2 3 x + 4 y}

= \frac{3}{2 3 x + 4 y}

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What is (\partial)/(\partial x)(sqrt(3x+4y)) ?
The answer to (\partial)/(\partial x)(sqrt(3x+4y)) is 3/(2sqrt(3x+4y))