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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int_{0}^{8} \frac{2}{x ^{\frac{2}{3}}} d x

\frac{d}{d x} (\frac{5}{x} - 1)

f (x) = x^{4} - 13 x^{2} + 36, at 1

\int \frac{x ^{2} - 3 x + 2}{x + 1} d x

\int \frac{5 y ^{4}}{y ^{5} - 13} d y

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