What is (\partial)/(\partial x)(sqrt(6x+3y)) ?

The answer to (\partial)/(\partial x)(sqrt(6x+3y)) is 3/(sqrt(6x+3y))

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(\partial)/(\partial x)(sqrt(6x+3y))

\frac{\partial}{\partial x} (6 x + 3 y)

\frac{3}{6 x + 3 y}

Solution steps

\frac{\partial}{\partial x} (6 x + 3 y)

Treat

y

as a constant

Apply the chain rule:

\frac{1}{2 6 x + 3 y} \frac{\partial}{\partial x} (6 x + 3 y)

= \frac{1}{2 6 x + 3 y} \frac{\partial}{\partial x} (6 x + 3 y)

\frac{\partial}{\partial x} (6 x + 3 y) = 6

= \frac{1}{2 6 x + 3 y} \cdot 6

Simplify

\frac{1}{2 6 x + 3 y} \cdot 6 : \frac{3}{6 x + 3 y}

= \frac{3}{6 x + 3 y}

\frac{d}{d x} (ln (x^{2} - 3))

y = 2 x^{4} - 16 x^{2} + 9, at x = - 4

y = \frac{2}{x}, (5, \frac{2}{5})

\int - 2 x^{- 3} d x

y^{2} = 2 x, x = 2 y

What is (\partial)/(\partial x)(sqrt(6x+3y)) ?
The answer to (\partial)/(\partial x)(sqrt(6x+3y)) is 3/(sqrt(6x+3y))