derivative of-2xsin(2x+cos(2x))

Lösung

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

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

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

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

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

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

Vereinfache

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

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

in v erse l a pl a ce \frac{( s + 1 )}{s ( s ^{2} + s + 1 )}

\frac{d y}{d x} + 1 = 2 y

\int e^{r} d r

\int (15 x^{- 1} - 4 sinh (x)) d x

\frac{d}{d x} ((x^{6} + 1)^{\frac{5}{2}})