derivative of (x^2-1(x^2-4)(x^2-9))

Lösung

\frac{d}{d x} ((x^{2} - 1) (x^{2} - 4) (x^{2} - 9))

6 x^{5} - 56 x^{3} + 98 x

Schritte zur Lösung

\frac{d}{d x} ((x^{2} - 1) (x^{2} - 4) (x^{2} - 9))

Wende die Produktregel an:

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

f = x^{2} - 1, g = (x^{2} - 4) (x^{2} - 9)

= \frac{d}{d x} (x^{2} - 1) (x^{2} - 4) (x^{2} - 9) + \frac{d}{d x} ((x^{2} - 4) (x^{2} - 9)) (x^{2} - 1)

\frac{d}{d x} (x^{2} - 1) = 2 x

\frac{d}{d x} ((x^{2} - 4) (x^{2} - 9)) = 4 x^{3} - 26 x

= 2 x (x^{2} - 4) (x^{2} - 9) + (4 x^{3} - 26 x) (x^{2} - 1)

Vereinfache

2 x (x^{2} - 4) (x^{2} - 9) + (4 x^{3} - 26 x) (x^{2} - 1) : 6 x^{5} - 56 x^{3} + 98 x

= 6 x^{5} - 56 x^{3} + 98 x

\frac{\partial}{\partial x} (50 - (4 x^{2} + y^{2}))

\frac{d}{d x} (1 - cos (x))

y^{'} = 0.0013 y (3000 - y)

t an g e n t y = 3 x^{3} - x^{2} + 7, (2, 27)

\int (x + 4) (x + 2) d x