derivative of (x+5(x-1)(x-7))

Lösung

\frac{d}{d x} ((x + 5) (x - 1) (x - 7))

3 x^{2} - 6 x - 33

Schritte zur Lösung

\frac{d}{d x} ((x + 5) (x - 1) (x - 7))

Wende die Produktregel an:

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

f = x + 5, g = (x - 1) (x - 7)

= \frac{d}{d x} (x + 5) (x - 1) (x - 7) + \frac{d}{d x} ((x - 1) (x - 7)) (x + 5)

\frac{d}{d x} (x + 5) = 1

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

= 1 \cdot (x - 1) (x - 7) + (2 x - 8) (x + 5)

Vereinfache

1 \cdot (x - 1) (x - 7) + (2 x - 8) (x + 5) : 3 x^{2} - 6 x - 33

= 3 x^{2} - 6 x - 33

\int sin^{5} (x co) s^{6} x d x

d er i v a t i v e f (x) = \frac{x ^{3} - 7 x ^{2} + 7}{x ^{2}}

\frac{\partial}{\partial x} (y^{6} sin (2 x))

x \to \infty lim (- 3 x)

\frac{d}{d x} (a + \frac{1}{x})