derivative of (3-x^2(x^3-x+1))

Lösung

\frac{d}{d x} ((3 - x^{2}) (x^{3} - x + 1))

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

Schritte zur Lösung

\frac{d}{d x} ((3 - x^{2}) (x^{3} - x + 1))

Wende die Produktregel an:

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

f = 3 - x^{2}, g = x^{3} - x + 1

= \frac{d}{d x} (3 - x^{2}) (x^{3} - x + 1) + \frac{d}{d x} (x^{3} - x + 1) (3 - x^{2})

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

\frac{d}{d x} (x^{3} - x + 1) = 3 x^{2} - 1

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

Vereinfache

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

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

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

\int \frac{x ^{4} + x ^{3} + x ^{2} + 1}{x ^{2} + x - 2} d x

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

\int \frac{8}{36 x ^{2} + 4} d x

\frac{d}{d x} (e^{- x} cos (\frac{x}{2}))