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

Lösung

ableitung von

y = \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}}

s im pl i f y 3 x^{- 2} - 4 x

d er i v a t i v e e^{1 + (l n (x))^{2}}

1 - y^{2} d x - 1 - x^{2} d y = 0, y (0) = \frac{1}{2}

y^{^{'}} = e^{t - y}

\int (3 x - 11) e^{x} d x