What is the derivative of ln((x+2/(x^2))) ?

The derivative of ln((x+2/(x^2))) is (-x-4)/(x(x+2))

What is the first derivative of ln((x+2/(x^2))) ?

The first derivative of ln((x+2/(x^2))) is (-x-4)/(x(x+2))

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

\frac{- x - 4}{x ( x + 2 )}

Solution steps

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

Apply the chain rule:

\frac{1}{\frac{x + 2}{x ^{2}}} \frac{d}{d x} (\frac{x + 2}{x ^{2}})

= \frac{1}{\frac{x + 2}{x ^{2}}} \frac{d}{d x} (\frac{x + 2}{x ^{2}})

\frac{d}{d x} (\frac{x + 2}{x ^{2}}) = \frac{- x - 4}{x ^{3}}

= \frac{1}{\frac{x + 2}{x ^{2}}} \cdot \frac{- x - 4}{x ^{3}}

Simplify

\frac{1}{\frac{x + 2}{x ^{2}}} \cdot \frac{- x - 4}{x ^{3}} : \frac{- x - 4}{x ( x + 2 )}

= \frac{- x - 4}{x ( x + 2 )}

\frac{d}{d x} (x^{2} y^{4})

x \to 2 lim (x^{2} - 5)

\int 3 x^{2} + cos (x) d x

x \to 0 lim (\frac{1 - e ^{- x}}{x})

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

What is the derivative of ln((x+2/(x^2))) ?
The derivative of ln((x+2/(x^2))) is (-x-4)/(x(x+2))
What is the first derivative of ln((x+2/(x^2))) ?
The first derivative of ln((x+2/(x^2))) is (-x-4)/(x(x+2))