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

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

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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d}{d x} (5 lo g_{2} (x))

y^{^{''}} + 10 y^{^{'}} + 25 y = 0, y (0) = 0, y (\frac{π}{2}) = 1

\frac{8}{( s - 1 ) ^{3}}

y^{^{'}} = \frac{1}{1 + x}

\int x^{3} x^{2} - 16 d x

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