derivative of (1+x^{-3})

Lösung

\frac{d}{d x} ((1 + x)^{- 3})

- \frac{3}{( 1 + x ) ^{4}}

Schritte zur Lösung

\frac{d}{d x} ((1 + x)^{- 3})

Wende die Kettenregel an:

- \frac{3}{( 1 + x ) ^{4}} \frac{d}{d x} (1 + x)

= - \frac{3}{( 1 + x ) ^{4}} \frac{d}{d x} (1 + x)

\frac{d}{d x} (1 + x) = 1

= - \frac{3}{( 1 + x ) ^{4}} \cdot 1

Vereinfache

= - \frac{3}{( 1 + x ) ^{4}}

\int (t + \frac{1}{t})^{\frac{3}{2}} (\frac{t ^{2} - 1}{t ^{2}}) d t

\int \frac{1}{e ^{2 y} - 1} d y

\int_{0}^{\frac{π}{4}} x^{2} sin (2 x) d x

d er i v a t i v e \frac{1}{4 x ^{2} + 3 x}

\int 36 e^{4 x} 3 + e^{4 x} d x