derivative f(x)= 4/((x^2+1)^2)

Lösung

ableitung von

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

- \frac{16 x}{( x ^{2} + 1 ) ^{3}}

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

- \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

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

Vereinfache

4 (- \frac{2}{( x ^{2} + 1 ) ^{3}} \cdot 2 x) : - \frac{16 x}{( x ^{2} + 1 ) ^{3}}

= - \frac{16 x}{( x ^{2} + 1 ) ^{3}}

\frac{d}{d x} (6 x - 9)

y^{^{'''}} - 9 y^{^{''}} + 20 y^{^{'}} = 0

\frac{d}{d x} (\frac{x}{x ^{2} + 36})

\frac{\partial}{\partial x} (x^{3} - 3 x y)

\int_{0}^{7} \frac{8}{9 x ^{2} + 10 x + 1} d x