derivative (x+3)(x-5)^7

Lösung

ableitung von

(x + 3) (x - 5)^{7}

(x - 5)^{7} + 7 (x - 5)^{6} (x + 3)

Schritte zur Lösung

\frac{d}{d x} ((x + 3) (x - 5)^{7})

Wende die Produktregel an:

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

f = x + 3, g = (x - 5)^{7}

= \frac{d}{d x} (x + 3) (x - 5)^{7} + \frac{d}{d x} ((x - 5)^{7}) (x + 3)

\frac{d}{d x} (x + 3) = 1

\frac{d}{d x} ((x - 5)^{7}) = 7 (x - 5)^{6}

= 1 \cdot (x - 5)^{7} + 7 (x - 5)^{6} (x + 3)

Vereinfache

= (x - 5)^{7} + 7 (x - 5)^{6} (x + 3)

x \to + 0 lim (\frac{x ^{2} - 5}{x - 2})

\frac{d y}{1 - y ^{2}} = d x

\frac{d y}{d t} = \frac{8 t y}{t ^{2} + 1}, y (0) = - 2

\int 15 x^{2} d x

\int sec^{2} (3 x) e^{t a n (3 x) - 2} d x