derivative derivative of 1/((1+x^2))

Lösung

ableitung von

\frac{d}{d 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}}

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

s l o p e (- 4, 2), (4, - 4)

d er i v a t i v e \frac{d}{d x} (sin (x^{2}))

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

d er i v a t i v e \frac{d}{d x} (sec^{2} (x))