What is the derivative of ln(sqrt(3x^2+1)) ?

The derivative of ln(sqrt(3x^2+1)) is (3x)/(3x^2+1)

What is the first derivative of ln(sqrt(3x^2+1)) ?

The first derivative of ln(sqrt(3x^2+1)) is (3x)/(3x^2+1)

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

\frac{3 x}{3 x ^{2} + 1}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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