What is the derivative of 1/((ln(x)^2)) ?

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

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

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

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

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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