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

Lösung

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

- sin (x - x^{2}) (1 - 2 x)^{2} - 2 cos (x - x^{2})

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

= (- sin (x - x^{2}) (1 - 2 x)) (1 - 2 x) + (- 2) cos (x - x^{2})

Vereinfache

(- sin (x - x^{2}) (1 - 2 x)) (1 - 2 x) + (- 2) cos (x - x^{2}) : - sin (x - x^{2}) (1 - 2 x)^{2} - 2 cos (x - x^{2})

= - sin (x - x^{2}) (1 - 2 x)^{2} - 2 cos (x - x^{2})

x \to 0 lim (\frac{1}{x} ln (1 - 2 x))

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

l a pl a ce t r an s f or m t e^{- 3 t} cos (3 t)

\frac{d}{d x} (\frac{80 - x}{4})

\int x sin^{2} (2 x) d x