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

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

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

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

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derivative of

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

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (ln (x) ln (x)) = \frac{2 ln ( x )}{x}

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

Simplify

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

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

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