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

Lösung

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

4 x cos (2 x) + 4 sin (2 x) - 4 cos (2 x)

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

= - (- sin (2 x) \cdot 2) - 2 (2 cos (2 x) (1 - x) - sin (2 x))

Vereinfache

- (- sin (2 x) \cdot 2) - 2 (2 cos (2 x) (1 - x) - sin (2 x)) : 4 x cos (2 x) + 4 sin (2 x) - 4 cos (2 x)

= 4 x cos (2 x) + 4 sin (2 x) - 4 cos (2 x)

x \frac{d y}{d x} + 2 y = x^{2}

x \to 0 lim (\frac{x}{sin ^{2} ( x )})

\frac{d}{d x} (\frac{x}{8 x + 3})

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

\int \frac{ln ( x )}{x ( 1 + ln ^{2} ( x ) )} d x