derivative of (x-4(x+1)(x+5))

Lösung

\frac{d}{d x} ((x - 4) (x + 1) (x + 5))

3 x^{2} + 4 x - 19

Schritte zur Lösung

\frac{d}{d x} ((x - 4) (x + 1) (x + 5))

Wende die Produktregel an:

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

f = x - 4, g = (x + 1) (x + 5)

= \frac{d}{d x} (x - 4) (x + 1) (x + 5) + \frac{d}{d x} ((x + 1) (x + 5)) (x - 4)

\frac{d}{d x} (x - 4) = 1

\frac{d}{d x} ((x + 1) (x + 5)) = 2 x + 6

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

Vereinfache

1 \cdot (x + 1) (x + 5) + (2 x + 6) (x - 4) : 3 x^{2} + 4 x - 19

= 3 x^{2} + 4 x - 19

d er i v a t i v e f (x) = \frac{x ^{3}}{3 - x ^{2}}

\int \frac{( 4 x - 5 ) ( 2 x - 7 )}{3} d x

\frac{\partial}{\partial x} (ln (x^{2} + 6 y^{2} + 8))

\frac{d y}{d x} = (y + 8)

\int \frac{sec ( θ )}{tan ( θ )} d θ