derivative of (x+1/x ^5)

Lösung

\frac{d}{d x} ((x + \frac{1}{x})^{5})

5 (x + \frac{1}{x})^{4} (1 - \frac{1}{x ^{2}})

Schritte zur Lösung

\frac{d}{d x} ((x + \frac{1}{x})^{5})

Wende die Kettenregel an:

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

= 5 (x + \frac{1}{x})^{4} \frac{d}{d x} (x + \frac{1}{x})

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

= 5 (x + \frac{1}{x})^{4} (1 - \frac{1}{x ^{2}})

\int_{0}^{\infty} u e^{- u^{2}} d u

in v erse l a pl a ce \frac{s}{s ^{2} + 10 s + 9.8}

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

x \to 1 + lim (\frac{ln ( x )}{x - 1})

x \to 0 lim (\frac{6}{x ^{2} + x} - \frac{6}{x})