What is the derivative of ln(x/(x^2+6)) ?

The derivative of ln(x/(x^2+6)) is (-x^2+6)/(x(x^2+6))

What is the first derivative of ln(x/(x^2+6)) ?

The first derivative of ln(x/(x^2+6)) is (-x^2+6)/(x(x^2+6))

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} + 6})

\frac{- x ^{2} + 6}{x ( x ^{2} + 6 )}

Solution steps

\frac{d}{d x} (ln (\frac{x}{x ^{2} + 6}))

Apply the chain rule:

\frac{1}{\frac{x}{x ^{2} + 6}} \frac{d}{d x} (\frac{x}{x ^{2} + 6})

= \frac{1}{\frac{x}{x ^{2} + 6}} \frac{d}{d x} (\frac{x}{x ^{2} + 6})

\frac{d}{d x} (\frac{x}{x ^{2} + 6}) = \frac{- x ^{2} + 6}{( x ^{2} + 6 ) ^{2}}

= \frac{1}{\frac{x}{x ^{2} + 6}} \cdot \frac{- x ^{2} + 6}{( x ^{2} + 6 ) ^{2}}

Simplify

\frac{1}{\frac{x}{x ^{2} + 6}} \cdot \frac{- x ^{2} + 6}{( x ^{2} + 6 ) ^{2}} : \frac{- x ^{2} + 6}{x ( x ^{2} + 6 )}

= \frac{- x ^{2} + 6}{x ( x ^{2} + 6 )}

\int \frac{- 1}{x} d x

y (x + 7) + y^{^{'}} = 0

\frac{d}{d x} (tan (5 x + 2))

\frac{d}{d x} (x^{3} \cdot e^{- x})

\frac{d}{d x} (x^{4} - 8 x^{3} + 22 x^{2} - 24 x + 9)

What is the derivative of ln(x/(x^2+6)) ?
The derivative of ln(x/(x^2+6)) is (-x^2+6)/(x(x^2+6))
What is the first derivative of ln(x/(x^2+6)) ?
The first derivative of ln(x/(x^2+6)) is (-x^2+6)/(x(x^2+6))