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

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

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

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

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derivative of

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

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d}{d x} y = 5 x

(- 4, 2), (4, - 4)

\frac{d}{d x} (sin (x^{2}))

\int (e^{x y}) d x

\frac{d}{d x} (sec^{2} (x))

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