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

Lösung

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

- 5 x^{4} + 4 x^{3} + 12 x^{2} - 8 x - 4

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

(- 1) (x^{2} - 2)^{2} + 4 x (x^{2} - 2) (1 - x) : - 5 x^{4} + 4 x^{3} + 12 x^{2} - 8 x - 4

= - 5 x^{4} + 4 x^{3} + 12 x^{2} - 8 x - 4

x \to - 1 + lim (\frac{5}{x + 1})

d er i v a t i v e f (x) = x^{5} e^{x}

\frac{\partial}{\partial x} (21 x^{3} cos (7 x^{2} y))

\int \frac{1}{x ^{2} - 16} d x

x \to + 2 - lim (6 - 3 x - 3)