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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d}{d x} (\frac{x ^{3}}{2} + \frac{1}{6 x})

x^{2} + 2 x - 6

\int x 2 x^{2} - 1 d x

\frac{d}{d t} (2 t - 3)

x \to 3 - lim (\frac{4 x}{x - 3})

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