derivative 8(x-1/x)^4

Lösung

ableitung von

8 (x - \frac{1}{x})^{4}

32 (x - \frac{1}{x})^{3} (1 + \frac{1}{x ^{2}})

Schritte zur Lösung

\frac{d}{d x} (8 (x - \frac{1}{x})^{4})

Entferne die Konstante:

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

= 8 \frac{d}{d x} ((x - \frac{1}{x})^{4})

Wende die Kettenregel an:

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

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

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

= 8 \cdot 4 (x - \frac{1}{x})^{3} (1 + \frac{1}{x ^{2}})

Vereinfache

= 32 (x - \frac{1}{x})^{3} (1 + \frac{1}{x ^{2}})

\int_{0}^{1} [(x^{2} - 1) - (- x + 2)] d x

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

\frac{d}{d x} (\frac{5 x}{4})

x \to 0 lim (x ln (x - 1))

a re a x^{2} - 2 x + 1, - x + 3