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

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

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

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

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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