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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\frac{d}{d x} (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 )}

\int (2 + sin^{2} (θ))^{2} cos (θ) d θ

y^{^{'}} - \frac{4}{x} y = 3 x - 2

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

x \to 0 lim (2^{x} + 6)

e^{2 x}, e^{x}, [0, 1]

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))