derivative f(x)=(x+1)(3x^2-5x+2)

Lösung

ableitung von

f (x) = (x + 1) (3 x^{2} - 5 x + 2)

9 x^{2} - 4 x - 3

Schritte zur Lösung

\frac{d}{d x} ((x + 1) (3 x^{2} - 5 x + 2))

Wende die Produktregel an:

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

f = x + 1, g = 3 x^{2} - 5 x + 2

= \frac{d}{d x} (x + 1) (3 x^{2} - 5 x + 2) + \frac{d}{d x} (3 x^{2} - 5 x + 2) (x + 1)

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

\frac{d}{d x} (3 x^{2} - 5 x + 2) = 6 x - 5

= 1 \cdot (3 x^{2} - 5 x + 2) + (6 x - 5) (x + 1)

Vereinfache

1 \cdot (3 x^{2} - 5 x + 2) + (6 x - 5) (x + 1) : 9 x^{2} - 4 x - 3

= 9 x^{2} - 4 x - 3

y^{^{''}} - y^{^{'}} - y = 0

x \to 4 lim (2 x - 1)

\frac{d}{d x} (2 e^{x} ln (x))

x \to - 2 lim (- x^{2} + 8 x - 4)

\int \frac{28}{( 1 - x ^{2} ) ^{\frac{3}{2}}} d x