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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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