What is the derivative of ln((x^2)/(3x+1)) ?

The derivative of ln((x^2)/(3x+1)) is (3x+2)/(x(3x+1))

What is the first derivative of ln((x^2)/(3x+1)) ?

The first derivative of ln((x^2)/(3x+1)) is (3x+2)/(x(3x+1))

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derivative of

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

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

Solution steps

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

Apply the chain rule:

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

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

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

= \frac{1}{\frac{x ^{2}}{3 x + 1}} \cdot \frac{3 x ^{2} + 2 x}{( 3 x + 1 ) ^{2}}

Simplify

\frac{1}{\frac{x ^{2}}{3 x + 1}} \cdot \frac{3 x ^{2} + 2 x}{( 3 x + 1 ) ^{2}} : \frac{3 x + 2}{x ( 3 x + 1 )}

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

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What is the derivative of ln((x^2)/(3x+1)) ?
The derivative of ln((x^2)/(3x+1)) is (3x+2)/(x(3x+1))
What is the first derivative of ln((x^2)/(3x+1)) ?
The first derivative of ln((x^2)/(3x+1)) is (3x+2)/(x(3x+1))