derivative of (x-1^2(x+3))

Lösung

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

3 x^{2} + 2 x - 5

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

\frac{d}{d x} (x + 3) = 1

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

Vereinfache

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

= 3 x^{2} + 2 x - 5

d er i v a t i v e m x + b

\frac{\partial}{\partial x} (- k p (x) gx + A)

\int_{0}^{2} a^{\frac{x}{2}} d x

\int - \frac{9}{x} d x

\int_{1}^{5} \frac{x ^{2} + 7}{6 x - x ^{2}} d x