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Popular Calculus >

derivative of ln(2x+3y)

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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Frequently Asked Questions (FAQ)

What is the derivative of ln(2x+3y) ?
The derivative of ln(2x+3y) is (2+3\frac{dy)/(dx)}{2x+3y}
What is the first derivative of ln(2x+3y) ?
The first derivative of ln(2x+3y) is (2+3\frac{dy)/(dx)}{2x+3y}