derivative of sin(4x-1/3 cos^2(4x))

Lösung

\frac{d}{d x} (sin (4 x) - \frac{1}{3} cos^{2} (4 x))

4 cos (4 x) + \frac{8}{3} cos (4 x) sin (4 x)

Schritte zur Lösung

\frac{d}{d x} (sin (4 x) - \frac{1}{3} cos^{2} (4 x))

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (sin (4 x)) - \frac{d}{d x} (\frac{1}{3} cos^{2} (4 x))

\frac{d}{d x} (sin (4 x)) = cos (4 x) \cdot 4

\frac{d}{d x} (\frac{1}{3} cos^{2} (4 x)) = - \frac{8}{3} cos (4 x) sin (4 x)

= cos (4 x) \cdot 4 - (- \frac{8}{3} cos (4 x) sin (4 x))

Vereinfache

= 4 cos (4 x) + \frac{8}{3} cos (4 x) sin (4 x)

\frac{\partial}{\partial x} (\frac{( a R ( x ) + b + c R ( x ) + d e + f ( x ) + g ( x ) e )}{x})

\int 12 x^{5} d x

\int_{0}^{5} ∣ 2 x - 5 ∣ d x

\frac{d}{d x} (2 x + 6)

\frac{\partial}{\partial x} (4 e^{x y})