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

The derivative of-1/(x^2+1) is 2/(x^3)

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

The first derivative of-1/(x^2+1) is 2/(x^3)

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

\frac{2}{x ^{3}}

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{d}{d x} (1) = 0

= - (- \frac{2}{x ^{3}}) + 0

Simplify

= \frac{2}{x ^{3}}

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What is the derivative of-1/(x^2+1) ?
The derivative of-1/(x^2+1) is 2/(x^3)
What is the first derivative of-1/(x^2+1) ?
The first derivative of-1/(x^2+1) is 2/(x^3)