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Popular >

derivative of ln(3x+5y)

Solution

\frac{d}{d x} (ln (3 x + 5 y))

Solution

\frac{3 + 5 \frac{d y}{d x}}{3 x + 5 y}

Solution steps

\frac{d}{d x} (ln (3 x + 5 y))

Apply the chain rule:

\frac{1}{3 x + 5 y} \frac{d}{d x} (3 x + 5 y)

= \frac{1}{3 x + 5 y} \frac{d}{d x} (3 x + 5 y)

\frac{d}{d x} (3 x + 5 y) = 3 + 5 \frac{d y}{d x}

= \frac{1}{3 x + 5 y} (3 + 5 \frac{d y}{d x})

Simplify

\frac{1}{3 x + 5 y} (3 + 5 \frac{d y}{d x}) : \frac{3 + 5 \frac{d y}{d x}}{3 x + 5 y}

= \frac{3 + 5 \frac{d y}{d x}}{3 x + 5 y}

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Frequently Asked Questions (FAQ)

What is the derivative of ln(3x+5y) ?
The derivative of ln(3x+5y) is (3+5\frac{dy)/(dx)}{3x+5y}
What is the first derivative of ln(3x+5y) ?
The first derivative of ln(3x+5y) is (3+5\frac{dy)/(dx)}{3x+5y}