What is the derivative of y= 2/(ln(x)) ?

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

What is the first derivative of y= 2/(ln(x)) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

y = \frac{2}{ln ( x )}

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

Solution steps

\frac{d}{d x} (\frac{2}{ln ( x )})

Take the constant out:

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

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

Apply exponent rule:

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

= 2 \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}

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

Simplify

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

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

f (x) = \frac{1}{x ^{7}}

f (t) = 2 t^{2}

f (t) = (3 t + 1)^{\frac{2}{3}}

\frac{d}{d x} (5^{s i n (x)})

\frac{d}{d x} (x^{2} cos^{2} (x))

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