What is the derivative of ln(9/x) ?

The derivative of ln(9/x) is -1/x

What is the first derivative of ln(9/x) ?

The first derivative of ln(9/x) is -1/x

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

ln (\frac{9}{x})

- \frac{1}{x}

Solution steps

\frac{d}{d x} (ln (\frac{9}{x}))

Apply the chain rule:

\frac{1}{\frac{9}{x}} \frac{d}{d x} (\frac{9}{x})

= \frac{1}{\frac{9}{x}} \frac{d}{d x} (\frac{9}{x})

\frac{d}{d x} (\frac{9}{x}) = - \frac{9}{x ^{2}}

= \frac{1}{\frac{9}{x}} (- \frac{9}{x ^{2}})

Simplify

\frac{1}{\frac{9}{x}} (- \frac{9}{x ^{2}}) : - \frac{1}{x}

= - \frac{1}{x}

d er i v a t i v e lo g_{10} (2^{x} + 2^{- x})

\frac{d}{d n} (i^{2 n})

d er i v a t i v e cot (x^{4})

d er i v a t i v e x^{2} (1 - m^{2})

d er i v a t i v e f (x) = 10 x^{2} + 5 x - 2

What is the derivative of ln(9/x) ?
The derivative of ln(9/x) is -1/x
What is the first derivative of ln(9/x) ?
The first derivative of ln(9/x) is -1/x