derivative (2x+5)(5x^2+1)

Lösung

ableitung von

(2 x + 5) (5 x^{2} + 1)

30 x^{2} + 50 x + 2

Schritte zur Lösung

\frac{d}{d x} ((2 x + 5) (5 x^{2} + 1))

Wende die Produktregel an:

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

f = 2 x + 5, g = 5 x^{2} + 1

= \frac{d}{d x} (2 x + 5) (5 x^{2} + 1) + \frac{d}{d x} (5 x^{2} + 1) (2 x + 5)

\frac{d}{d x} (2 x + 5) = 2

\frac{d}{d x} (5 x^{2} + 1) = 10 x

= 2 (5 x^{2} + 1) + 10 x (2 x + 5)

Vereinfache

2 (5 x^{2} + 1) + 10 x (2 x + 5) : 30 x^{2} + 50 x + 2

= 30 x^{2} + 50 x + 2

\int_{0}^{\frac{3 π}{2}} 7 ∣ sin (x) ∣ d x

a re a f (x) = e^{x}, g (x) = cos (x), x = 0, x = \frac{π}{2}

a re a y = x^{2} - 3 x, y = x

\int_{0}^{2} x (1 - x) d x

x \to - \infty lim (1 + e^{x})