What is the derivative of (15/(ln(x))) ?

The derivative of (15/(ln(x))) is -(15)/(xln^2(x))

What is the first derivative of (15/(ln(x))) ?

The first derivative of (15/(ln(x))) is -(15)/(xln^2(x))

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\frac{d}{d x} (\frac{15}{ln ( x )})

- \frac{15}{x ln ^{2} ( x )}

Solution steps

\frac{d}{d x} (\frac{15}{ln ( x )})

Take the constant out:

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

= 15 \frac{d}{d x} (\frac{1}{ln ( x )})

Apply exponent rule:

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

= 15 \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}

= 15 (- \frac{1}{( ln ( x ) ) ^{2}} \cdot \frac{1}{x})

Simplify

15 (- \frac{1}{ln ^{2} ( x )} \cdot \frac{1}{x}) : - \frac{15}{x ln ^{2} ( x )}

= - \frac{15}{x ln ^{2} ( x )}

What is the derivative of (15/(ln(x))) ?
The derivative of (15/(ln(x))) is -(15)/(xln^2(x))
What is the first derivative of (15/(ln(x))) ?
The first derivative of (15/(ln(x))) is -(15)/(xln^2(x))