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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

= \frac{1}{3 x ^{2} + 2} \cdot 6 x

Simplify

\frac{1}{3 x ^{2} + 2} \cdot 6 x : \frac{6 x}{3 x ^{2} + 2}

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

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