What is the derivative of ln(x/(x^2+1)) ?

The derivative of ln(x/(x^2+1)) is (-x^2+1)/(x(x^2+1))

What is the first derivative of ln(x/(x^2+1)) ?

The first derivative of ln(x/(x^2+1)) is (-x^2+1)/(x(x^2+1))

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derivative of

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{3 s + 1}{s ^{2} ( s ^{2} + 4 )}

x y^{^{'}} - y = \frac{x ^{2}}{y ^{2}}

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

25

4 - x^{2}, 3 x

What is the derivative of ln(x/(x^2+1)) ?
The derivative of ln(x/(x^2+1)) is (-x^2+1)/(x(x^2+1))
What is the first derivative of ln(x/(x^2+1)) ?
The first derivative of ln(x/(x^2+1)) is (-x^2+1)/(x(x^2+1))