derivative (x-5)(x+4)(x+6)

Lösung

ableitung von

(x - 5) (x + 4) (x + 6)

3 x^{2} + 10 x - 26

Schritte zur Lösung

\frac{d}{d x} ((x - 5) (x + 4) (x + 6))

Wende die Produktregel an:

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

f = x - 5, g = (x + 4) (x + 6)

= \frac{d}{d x} (x - 5) (x + 4) (x + 6) + \frac{d}{d x} ((x + 4) (x + 6)) (x - 5)

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

\frac{d}{d x} ((x + 4) (x + 6)) = 2 x + 10

= 1 \cdot (x + 4) (x + 6) + (2 x + 10) (x - 5)

Vereinfache

1 \cdot (x + 4) (x + 6) + (2 x + 10) (x - 5) : 3 x^{2} + 10 x - 26

= 3 x^{2} + 10 x - 26

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

\int_{0}^{\infty} u^{2} e^{- u} d u

\frac{\partial}{\partial y} (z - x^{2} + y^{2})

d er i v a t i v e - 3 e^{x^{5}}

\int \frac{( x - 1 )}{( x + 1 )} d x