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

Lösung

ableitung von

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

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

- \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

Vereinfache

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

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

d er i v a t i v e \frac{x ^{2} - 3 x + 2}{- x ^{2} - 4 x - 4}

\frac{\partial}{\partial x} (ln (sin (x)))

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

\int (x^{2} + x) e^{- 2 x} d x

\frac{d y}{d x} = \frac{x ^{2} - y ^{2}}{x y}, y (2) = 2