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

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

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

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

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derivative of

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

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

Solution steps

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

5 x, x^{2}

x \to 0 lim (\frac{x}{x + 2})

\int sec^{4} (x) tan^{8} (x) d x

\int (x^{3} - 2 sin (3 x))^{2} d x

x \to \infty lim (\frac{e ^{2 x} - e ^{x}}{ln ( x + 1 )})

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