derivative of x^7+1/(x^7+7x+7/x+7)

Lösung

\frac{d}{d x} (x^{7} + \frac{1}{x ^{7}} + 7 x + \frac{7}{x} + 7)

7 x^{6} - \frac{7}{x ^{8}} - \frac{7}{x ^{2}} + 7

Schritte zur Lösung

\frac{d}{d x} (x^{7} + \frac{1}{x ^{7}} + 7 x + \frac{7}{x} + 7)

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (x^{7}) + \frac{d}{d x} (\frac{1}{x ^{7}}) + \frac{d}{d x} (7 x) + \frac{d}{d x} (\frac{7}{x}) + \frac{d}{d x} (7)

\frac{d}{d x} (x^{7}) = 7 x^{6}

\frac{d}{d x} (\frac{1}{x ^{7}}) = - \frac{7}{x ^{8}}

\frac{d}{d x} (7 x) = 7

\frac{d}{d x} (\frac{7}{x}) = - \frac{7}{x ^{2}}

\frac{d}{d x} (7) = 0

= 7 x^{6} - \frac{7}{x ^{8}} + 7 - \frac{7}{x ^{2}} + 0

Vereinfache

= 7 x^{6} - \frac{7}{x ^{8}} - \frac{7}{x ^{2}} + 7

\frac{d y}{d t} - 2 y = e^{2 t}

d er i v a t i v e arctan (x)

n \to \infty lim (\frac{3 n}{n})

\int \frac{x - 2}{3 x + 6} d x

\int \frac{x ^{3}}{x ^{2} - 36} d x