derivative (x^2-18)(2x+3)

Lösung

ableitung von

(x^{2} - 18) (2 x + 3)

6 x^{2} + 6 x - 36

Schritte zur Lösung

\frac{d}{d x} ((x^{2} - 18) (2 x + 3))

Wende die Produktregel an:

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

f = x^{2} - 18, g = 2 x + 3

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

\frac{d}{d x} (x^{2} - 18) = 2 x

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

= 2 x (2 x + 3) + 2 (x^{2} - 18)

Vereinfache

2 x (2 x + 3) + 2 (x^{2} - 18) : 6 x^{2} + 6 x - 36

= 6 x^{2} + 6 x - 36

\int x + \frac{1}{x ^{2}} d x

\frac{\partial}{\partial x} (x y - 1)

\frac{\partial}{\partial y} ((x^{2} - 1) (y + 2))

t an g e n t f (x) = \frac{3}{x ^{2}}, at x = 1

\int_{0}^{\frac{π}{4}} 4 sin^{2} (x) d x