derivative of cos(2xsin(x/3))

Lösung

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

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

Schritte zur Lösung

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

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = cos (2 x), g = sin (\frac{x}{3})

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

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

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

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

Vereinfache

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

x \to + 4 lim (\frac{3 x}{4} + 2)

\frac{\partial}{\partial x} (2 e^{x^{8} y})

x \to 0 lim (x cos (\frac{9}{x}))

\frac{d ^{2}}{d x ^{2}} (\frac{7}{8 t ^{5}})

x \to 1 - lim (x - 2)