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

The answer to (\partial)/(\partial x)(sqrt(2x+3y)) is 1/(sqrt(2x+3y))

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

x \to \infty lim (\frac{3}{3})

\frac{d}{d x} (x^{l n (5)})

n = 0 \sum \infty \frac{1}{n ^{2} + 5 n + 6}

\int (5 x^{2} + 6 + \frac{9}{x ^{2} + 1}) d x

\frac{d h}{d t} + \frac{1}{2} h = 1

What is (\partial)/(\partial x)(sqrt(2x+3y)) ?
The answer to (\partial)/(\partial x)(sqrt(2x+3y)) is 1/(sqrt(2x+3y))