derivative (x^3-4x)(2x^2+5x)

Lösung

ableitung von

(x^{3} - 4 x) (2 x^{2} + 5 x)

10 x^{4} + 20 x^{3} - 24 x^{2} - 40 x

Schritte zur Lösung

\frac{d}{d x} ((x^{3} - 4 x) (2 x^{2} + 5 x))

Wende die Produktregel an:

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

f = x^{3} - 4 x, g = 2 x^{2} + 5 x

= \frac{d}{d x} (x^{3} - 4 x) (2 x^{2} + 5 x) + \frac{d}{d x} (2 x^{2} + 5 x) (x^{3} - 4 x)

\frac{d}{d x} (x^{3} - 4 x) = 3 x^{2} - 4

\frac{d}{d x} (2 x^{2} + 5 x) = 4 x + 5

= (3 x^{2} - 4) (2 x^{2} + 5 x) + (4 x + 5) (x^{3} - 4 x)

Vereinfache

(3 x^{2} - 4) (2 x^{2} + 5 x) + (4 x + 5) (x^{3} - 4 x) : 10 x^{4} + 20 x^{3} - 24 x^{2} - 40 x

= 10 x^{4} + 20 x^{3} - 24 x^{2} - 40 x

\int e^{t (a - s)} d t

\int_{0}^{1} cos^{2} (3 π x) d x

\frac{\partial}{\partial z} (3 x^{\frac{y}{z}})

d er i v a t i v e e^{x} \frac{( 2 x + 5 ) ^{2}}{x - 2}

y^{^{'}} = - 2 y + x