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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

x \to 0 + lim ((x + 1)^{l n (x)})

\frac{d}{d x} (ln (e^{4 x + 1}))

\frac{\partial}{\partial x} (\frac{5 x y}{10 x - y})

x \to \frac{π}{2} lim (x sec (x))

\frac{4}{s ( s + 2 ) ^{3}}

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