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Popular Calculus >

derivative of ln(5x+ln(3x))

Solution

derivative of

ln (5 x + ln (3 x))

Solution

\frac{5 x + 1}{x ( 5 x + ln ( 3 x ) )}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of ln(5x+ln(3x)) ?
The derivative of ln(5x+ln(3x)) is (5x+1)/(x(5x+ln(3x)))
What is the first derivative of ln(5x+ln(3x)) ?
The first derivative of ln(5x+ln(3x)) is (5x+1)/(x(5x+ln(3x)))