What is the derivative of ln(6x^3+3x^2-2x) ?

The derivative of ln(6x^3+3x^2-2x) is (18x^2+6x-2)/(6x^3+3x^2-2x)

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

The first derivative of ln(6x^3+3x^2-2x) is (18x^2+6x-2)/(6x^3+3x^2-2x)

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

\frac{18 x ^{2} + 6 x - 2}{6 x ^{3} + 3 x ^{2} - 2 x}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (6 x^{3} + 3 x^{2} - 2 x) = 18 x^{2} + 6 x - 2

= \frac{1}{6 x ^{3} + 3 x ^{2} - 2 x} (18 x^{2} + 6 x - 2)

Simplify

\frac{1}{6 x ^{3} + 3 x ^{2} - 2 x} (18 x^{2} + 6 x - 2) : \frac{18 x ^{2} + 6 x - 2}{6 x ^{3} + 3 x ^{2} - 2 x}

= \frac{18 x ^{2} + 6 x - 2}{6 x ^{3} + 3 x ^{2} - 2 x}

What is the derivative of ln(6x^3+3x^2-2x) ?
The derivative of ln(6x^3+3x^2-2x) is (18x^2+6x-2)/(6x^3+3x^2-2x)
What is the first derivative of ln(6x^3+3x^2-2x) ?
The first derivative of ln(6x^3+3x^2-2x) is (18x^2+6x-2)/(6x^3+3x^2-2x)