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))

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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 )}

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))