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

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

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

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

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derivative of

y = 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{d}{d x} (3^{2 x - 1})

\int \frac{1}{( x ^{2} - 25 ) ^{2}} d x

f (x) = x^{2} + 5, at x = 5

x \to 3 lim (2)

\frac{d}{d x} (π)

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