What is the derivative of f(x)= 5/(ln(x)) ?

The derivative of f(x)= 5/(ln(x)) is -5/(xln^2(x))

What is the first derivative of f(x)= 5/(ln(x)) ?

The first derivative of f(x)= 5/(ln(x)) is -5/(xln^2(x))

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derivative of

f (x) = \frac{5}{ln ( x )}

- \frac{5}{x ln ^{2} ( x )}

Solution steps

\frac{d}{d x} (\frac{5}{ln ( x )})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 5 \frac{d}{d x} (\frac{1}{ln ( x )})

Apply exponent rule:

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

= 5 \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}

= 5 (- \frac{1}{( ln ( x ) ) ^{2}} \cdot \frac{1}{x})

Simplify

5 (- \frac{1}{ln ^{2} ( x )} \cdot \frac{1}{x}) : - \frac{5}{x ln ^{2} ( x )}

= - \frac{5}{x ln ^{2} ( x )}

What is the derivative of f(x)= 5/(ln(x)) ?
The derivative of f(x)= 5/(ln(x)) is -5/(xln^2(x))
What is the first derivative of f(x)= 5/(ln(x)) ?
The first derivative of f(x)= 5/(ln(x)) is -5/(xln^2(x))