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

Lösung

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

- 70 x - 2

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

= 5 (1 - 7 x) + (- 7) (1 + 5 x)

Vereinfache

5 (1 - 7 x) + (- 7) (1 + 5 x) : - 70 x - 2

= - 70 x - 2

\frac{d}{d x} ((lo g_{e} (x))^{x})

y^{^{''}} + 7 y^{^{'}} + 10 y = 0, y (0) = 1, y^{^{'}} (0) = 0

\int \frac{1}{x - 5 3 x} d x

x \to 0 lim (\frac{2}{3 + 4 ^{\frac{1}{x}}})

a re a y = x^{3} + 1, (- 1, 2)