derivative x^7(1-2/(x+4))

Lösung

ableitung von

x^{7} (1 - \frac{2}{x + 4})

\frac{7 x ^{8} + 44 x ^{7} + 56 x ^{6}}{( x + 4 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (x^{7} (1 - \frac{2}{x + 4}))

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{7}, g = 1 - \frac{2}{x + 4}

= \frac{d}{d x} (x^{7}) (1 - \frac{2}{x + 4}) + \frac{d}{d x} (1 - \frac{2}{x + 4}) x^{7}

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

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

= 7 x^{6} (1 - \frac{2}{x + 4}) + \frac{2}{( x + 4 ) ^{2}} x^{7}

Vereinfache

7 x^{6} (1 - \frac{2}{x + 4}) + \frac{2}{( x + 4 ) ^{2}} x^{7} : \frac{7 x ^{8} + 44 x ^{7} + 56 x ^{6}}{( x + 4 ) ^{2}}

= \frac{7 x ^{8} + 44 x ^{7} + 56 x ^{6}}{( x + 4 ) ^{2}}

\frac{d}{d x} ((2 x - 6)^{4} (x^{2} + x + 1)^{5})

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

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

\int x (arctan (x))^{2} d x

\int \frac{tan ( x )}{cos ^{3} ( x )} d x