derivative of 1/(x^2+c)

Lösung

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

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

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

x \to 0 + lim (x e^{- \frac{2}{x}})

y^{^{'}} + 2 t y = e^{- t^{2}}

\int_{0}^{π} 6 cos^{2} (3 x) d x

\int (x^{2} - 4 x + 5)^{2} d x