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

The (1/(x(ln(x))^2))^' is -(ln(x)+2)/(x^2ln^3(x))

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

The first (1/(x(ln(x))^2))^' is -(ln(x)+2)/(x^2ln^3(x))

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

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

Solution steps

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

Apply exponent rule:

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

= ((x (ln (x))^{2})^{- 1})^{^{'}}

Apply the chain rule:

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

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

(x (ln (x))^{2})^{'} = ln^{2} (x) + 2 ln (x)

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

\frac{\partial}{\partial x} (\frac{x ^{2}}{2})

\frac{d}{d x} ((x + 1)^{3})

\int_{0}^{1} \frac{61}{x ^{5}} d x

\int_{- 1}^{1} (3 x^{2} + 1)^{2} d x

\int \frac{- 4}{x ^{2}} d x

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