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

Lösung

\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}})

Entferne die Konstante:

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

= - \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 y} (4 y^{2})

ma c l a u r in ln (x + x^{2} - 1)

\frac{d}{d x} (6 x + 6 x^{2})

\frac{d v}{d t} = 0.025 \cdot 7 - \frac{v}{2000}, v (0) = 100

\int_{4}^{10} 0.13 x d x