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

The derivative of 1/((x^2+1^2)) is -(4x)/((x^2+1)^3)

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

The first derivative of 1/((x^2+1^2)) is -(4x)/((x^2+1)^3)

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

- \frac{4 x}{( x ^{2} + 1 ) ^{3}}

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

- \frac{2}{( x ^{2} + 1 ) ^{3}} \cdot 2 x : - \frac{4 x}{( x ^{2} + 1 ) ^{3}}

= - \frac{4 x}{( x ^{2} + 1 ) ^{3}}

\frac{\partial}{\partial u} (ln (u cos (v)))

x \to 0 lim (\frac{sin ^{7} ( x )}{x})

y^{^{''}} + 4 y = \frac{4}{cos ( 2 t )}

\int - t e^{- t} d t

\int (8 + x^{3})^{5} (3 x^{2}) d x

What is the derivative of 1/((x^2+1^2)) ?
The derivative of 1/((x^2+1^2)) is -(4x)/((x^2+1)^3)
What is the first derivative of 1/((x^2+1^2)) ?
The first derivative of 1/((x^2+1^2)) is -(4x)/((x^2+1)^3)