derivative x(x^2+6)(x+9)

Lösung

ableitung von

x (x^{2} + 6) (x + 9)

4 x^{3} + 27 x^{2} + 12 x + 54

Schritte zur Lösung

\frac{d}{d x} (x (x^{2} + 6) (x + 9))

Wende die Produktregel an:

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

f = x, g = (x^{2} + 6) (x + 9)

= \frac{d x}{d x} (x^{2} + 6) (x + 9) + \frac{d}{d x} ((x^{2} + 6) (x + 9)) x

\frac{d x}{d x} = 1

\frac{d}{d x} ((x^{2} + 6) (x + 9)) = 3 x^{2} + 18 x + 6

= 1 \cdot (x^{2} + 6) (x + 9) + (3 x^{2} + 18 x + 6) x

Vereinfache

1 \cdot (x^{2} + 6) (x + 9) + (3 x^{2} + 18 x + 6) x : 4 x^{3} + 27 x^{2} + 12 x + 54

= 4 x^{3} + 27 x^{2} + 12 x + 54

t an g e n t f (x) = e^{4 x} cos (π x), at x = 0

t a y l or cos (3 x)

\int x^{9} + 8 d x

x y^{^{'}} = 7

\frac{\partial}{\partial y} (3 x^{2} e^{x^{2} y})