What is the derivative of ln(3x^2-x) ?

The derivative of ln(3x^2-x) is (6x-1)/(3x^2-x)

What is the first derivative of ln(3x^2-x) ?

The first derivative of ln(3x^2-x) is (6x-1)/(3x^2-x)

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

\frac{6 x - 1}{3 x ^{2} - x}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (3 x^{2} - x) = 6 x - 1

= \frac{1}{3 x ^{2} - x} (6 x - 1)

Simplify

\frac{1}{3 x ^{2} - x} (6 x - 1) : \frac{6 x - 1}{3 x ^{2} - x}

= \frac{6 x - 1}{3 x ^{2} - x}

x \to + 9 - lim (\frac{- 7}{( x + 9 )})

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What is the derivative of ln(3x^2-x) ?
The derivative of ln(3x^2-x) is (6x-1)/(3x^2-x)
What is the first derivative of ln(3x^2-x) ?
The first derivative of ln(3x^2-x) is (6x-1)/(3x^2-x)