derivative of 12cos(2x+pi/6)

Lösung

\frac{d}{d x} (12 cos (2 x + \frac{π}{6}))

12 (- 3 sin (2 x) - cos (2 x))

Schritte zur Lösung

\frac{d}{d x} (12 cos (2 x + \frac{π}{6}))

Vereinfache

12 cos (2 x + \frac{π}{6}) : 12 (\frac{3}{2} cos (2 x) - \frac{1}{2} sin (2 x))

= \frac{d}{d x} (12 (\frac{3}{2} cos (2 x) - \frac{1}{2} sin (2 x)))

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 12 \frac{d}{d x} (\frac{3}{2} cos (2 x) - \frac{1}{2} sin (2 x))

Wende die Summen-/Differenzregel an:

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

= 12 (\frac{d}{d x} (\frac{3}{2} cos (2 x)) - \frac{d}{d x} (\frac{1}{2} sin (2 x)))

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

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

= 12 (- 3 sin (2 x) - cos (2 x))

t \to - \infty lim (e^{3 t})

im pl i c i t \frac{d y}{d x}, x^{2} e^{y} - y^{4} = e^{x}

\int 2 x (x^{2} + 7)^{8} d x

\frac{d}{d x} (e^{x} sin (e^{x}))

\frac{d}{d t} (e^{3 c o s (t) + 2 t^{2}})