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

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

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

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

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derivative of

f (x) = 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 )}

x \to 3 - lim (e^{\frac{2}{x - 3}})

\int 5^{t} sin (5^{t}) d t

\int x (ln^{2} (x)) d x

n = 1 \sum \infty (\frac{n}{n + 10})^{n}

2 x y^{^{'}} = y^{2}

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