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

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

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

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

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derivative of

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

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d}{d x} (\frac{3 - x e ^{x}}{x + e ^{x}})

\frac{d}{d x} (cos (2 x) sin (3 x))

\int (7 x^{6} - \frac{6}{x ^{6}}) d x

\int x^{2} - 3 x + 8 d x

(- 7, - 6), (10, 8)

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