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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (1 + \frac{1}{x ^{2}}) = - \frac{2}{x ^{3}}

= \frac{1}{1 + \frac{1}{x ^{2}}} (- \frac{2}{x ^{3}})

Simplify

\frac{1}{1 + \frac{1}{x ^{2}}} (- \frac{2}{x ^{3}}) : - \frac{2}{x ( x ^{2} + 1 )}

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

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