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

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

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

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

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derivative of

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

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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