derivative f(x)=(x-1)(x^2-8x+7)

Lösung

ableitung von

f (x) = (x - 1) (x^{2} - 8 x + 7)

3 x^{2} - 18 x + 15

Schritte zur Lösung

\frac{d}{d x} ((x - 1) (x^{2} - 8 x + 7))

Wende die Produktregel an:

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

f = x - 1, g = x^{2} - 8 x + 7

= \frac{d}{d x} (x - 1) (x^{2} - 8 x + 7) + \frac{d}{d x} (x^{2} - 8 x + 7) (x - 1)

\frac{d}{d x} (x - 1) = 1

\frac{d}{d x} (x^{2} - 8 x + 7) = 2 x - 8

= 1 \cdot (x^{2} - 8 x + 7) + (2 x - 8) (x - 1)

Vereinfache

1 \cdot (x^{2} - 8 x + 7) + (2 x - 8) (x - 1) : 3 x^{2} - 18 x + 15

= 3 x^{2} - 18 x + 15

d er i v a t i v e f (x) = \frac{- cos ( x )}{4 x ^{2} + 2 x - 3}

in v erse l a pl a ce \frac{1}{( s - 5 ) ^{3}}

\frac{\partial}{\partial x} (56 e^{8 x} y)

\int_{0}^{\frac{π}{2}} (sin (2 x)) d x

x \to 1 - lim (2 x^{3} + 5 x)