What is the derivative of ln(x+ln(x)) ?

The derivative of ln(x+ln(x)) is (x+1)/(x(x+ln(x)))

What is the first derivative of ln(x+ln(x)) ?

The first derivative of ln(x+ln(x)) is (x+1)/(x(x+ln(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} (ln (x + ln (x)))

\frac{x + 1}{x ( x + ln ( x ) )}

Solution steps

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

Apply the chain rule:

\frac{1}{x + ln ( x )} \frac{d}{d x} (x + ln (x))

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

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

= \frac{1}{x + ln ( x )} (1 + \frac{1}{x})

Simplify

\frac{1}{x + ln ( x )} (1 + \frac{1}{x}) : \frac{x + 1}{x ( x + ln ( x ) )}

= \frac{x + 1}{x ( x + ln ( x ) )}

\frac{d}{d x} (1 - e^{- \frac{x}{2}})

\frac{1}{x - 5}

\frac{d}{d x} ((3 x + 2)^{3})

\int_{0}^{1} 5 ln (x) d x

f (x) = x \cdot e^{- x + 1}

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