en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of y=ln(8+ln(x))

Solution

derivative of

y = ln (8 + ln (x))

Solution

\frac{1}{x ( 8 + ln ( x ) )}

Solution steps

\frac{d}{d x} (ln (8 + ln (x)))

Apply the chain rule:

\frac{1}{8 + ln ( x )} \frac{d}{d x} (8 + ln (x))

= \frac{1}{8 + ln ( x )} \frac{d}{d x} (8 + ln (x))

\frac{d}{d x} (8 + ln (x)) = \frac{1}{x}

= \frac{1}{8 + ln ( x )} \cdot \frac{1}{x}

Simplify

\frac{1}{8 + ln ( x )} \cdot \frac{1}{x} : \frac{1}{x ( 8 + ln ( x ) )}

= \frac{1}{x ( 8 + ln ( x ) )}

Popular Examples

integral of 1/(sqrt(x^2-196))

\int \frac{1}{x ^{2} - 196} d x

limit as x approaches 0+of ln(1/(5x))

x \to 0 + lim (ln (\frac{1}{5 x}))

integral of sin(x)cos(x)sqrt(1+cos^2(x))

\int sin (x) cos (x) 1 + cos^{2} (x) d x

limit as x approaches 0 of e^{-7x}

x \to 0 lim (e^{- 7 x})

limit as x approaches 4 of x^2(-16x)/(x-4)

x \to 4 lim (x^{2} \frac{- 16 x}{x - 4})

Frequently Asked Questions (FAQ)

What is the derivative of y=ln(8+ln(x)) ?
The derivative of y=ln(8+ln(x)) is 1/(x(8+ln(x)))
What is the first derivative of y=ln(8+ln(x)) ?
The first derivative of y=ln(8+ln(x)) is 1/(x(8+ln(x)))