What is the derivative of 1/(ln(1+3x)) ?

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

What is the first derivative of 1/(ln(1+3x)) ?

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

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derivative of

\frac{1}{ln ( 1 + 3 x )}

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

Solution steps

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

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

= - \frac{1}{( ln ( 1 + 3 x ) ) ^{2}} \cdot \frac{3}{1 + 3 x}

Simplify

- \frac{1}{ln ^{2} ( 1 + 3 x )} \cdot \frac{3}{1 + 3 x} : - \frac{3}{ln ^{2} ( 1 + 3 x ) ( 1 + 3 x )}

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

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