derivative of cos(2xcos(x))

Lösung

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

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = cos (2 x), g = cos (x)

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

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

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

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

Vereinfache

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

\int \frac{8 - 3 x}{25 - 64 x ^{2}} d x

d er i v a t i v e (x - 3) (x^{2} + 6)

\frac{\partial}{\partial x} (8 x cos (x) cos (y))

x \to 1 lim (\frac{∣ x ∣}{x})

x \to 0 lim (h (\frac{1}{x}))