derivative x^7(x^2-3/(x^3))

Lösung

ableitung von

x^{7} (x^{2} - \frac{3}{x ^{3}})

9 x^{8} - 12 x^{3}

Schritte zur Lösung

\frac{d}{d x} (x^{7} (x^{2} - \frac{3}{x ^{3}}))

Wende die Produktregel an:

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

f = x^{7}, g = x^{2} - \frac{3}{x ^{3}}

= \frac{d}{d x} (x^{7}) (x^{2} - \frac{3}{x ^{3}}) + \frac{d}{d x} (x^{2} - \frac{3}{x ^{3}}) x^{7}

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

\frac{d}{d x} (x^{2} - \frac{3}{x ^{3}}) = 2 x + \frac{9}{x ^{4}}

= 7 x^{6} (x^{2} - \frac{3}{x ^{3}}) + (2 x + \frac{9}{x ^{4}}) x^{7}

Vereinfache

7 x^{6} (x^{2} - \frac{3}{x ^{3}}) + (2 x + \frac{9}{x ^{4}}) x^{7} : 9 x^{8} - 12 x^{3}

= 9 x^{8} - 12 x^{3}

n = 0 \sum \infty \frac{1}{n \cdot 2 ^{n}}

k = 0 \sum \infty \frac{1}{k ^{2} + 1}

2 x y d x = (1 + y) d y

\frac{\partial}{\partial y} (x^{3} - 3 x y^{2} + y^{3})

d er i v a t i v e f (x) = \frac{2 t + 3}{t + 5}