What is the derivative of (12/(ln(x))) ?

The derivative of (12/(ln(x))) is -(12)/(xln^2(x))

What is the first derivative of (12/(ln(x))) ?

The first derivative of (12/(ln(x))) is -(12)/(xln^2(x))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{d}{d x} (\frac{12}{ln ( x )})

- \frac{12}{x ln ^{2} ( x )}

Solution steps

\frac{d}{d x} (\frac{12}{ln ( x )})

Take the constant out:

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

= 12 \frac{d}{d x} (\frac{1}{ln ( x )})

Apply exponent rule:

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

= 12 \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}

= 12 (- \frac{1}{( ln ( x ) ) ^{2}} \cdot \frac{1}{x})

Simplify

12 (- \frac{1}{ln ^{2} ( x )} \cdot \frac{1}{x}) : - \frac{12}{x ln ^{2} ( x )}

= - \frac{12}{x ln ^{2} ( x )}

\int \frac{8 t ^{3} - 3 t ^{2} + 8 t}{t ^{2} + 1} d t

\int - 0.09 t d t

\frac{d}{d x} (e^{- 5 x^{3} - 2 x^{2}})

x \to 4 + lim (\frac{1}{( x - 4 ) ^{2}})

\int \frac{x}{1 + x ^{2} y ^{2}} d y

What is the derivative of (12/(ln(x))) ?
The derivative of (12/(ln(x))) is -(12)/(xln^2(x))
What is the first derivative of (12/(ln(x))) ?
The first derivative of (12/(ln(x))) is -(12)/(xln^2(x))