What is (\partial)/(\partial x)(sqrt(3x+2y)) ?

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

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(\partial)/(\partial x)(sqrt(3x+2y))

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int \frac{1}{9 x ^{2} + 6 x - 8} d x

n = 0 \sum \infty n \frac{1}{5 ^{n}}

\int sec^{2} (3 x t a) n^{5} 3 x d x

y ln (x) \frac{d y}{d x} = (\frac{( y + 1 )}{x})^{2}

(x^{2} - 7)^{2}

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