derivative of sin(x-pi/6)

Lösung

\frac{d}{d x} (sin (x - \frac{π}{6}))

\frac{3}{2} cos (x) + \frac{1}{2} sin (x)

Schritte zur Lösung

\frac{d}{d x} (sin (x - \frac{π}{6}))

Vereinfache

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

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

Wende die Summen-/Differenzregel an:

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

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

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

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

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

Vereinfache

= \frac{3}{2} cos (x) + \frac{1}{2} sin (x)

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

d er i v a t i v e (4 t^{4} + \frac{4}{t ^{4}})^{\frac{1}{4}}

(e^{2 x} + 4) \frac{d y}{d x} = y

f (x) = (cos (x))^{33} x

\frac{d}{d x} (sin (x) cos (y))