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

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

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

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

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

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

y = tan (12 x^{2}), at x = π

(x^{2})^{2}

sec^{2} (0)

n = 1 \sum \infty \frac{2}{n ^{6}}

\int \frac{x ^{4} - 3 x ^{2} + 4 x}{5 x} d x

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