derivative of cos(2xsin(x))

Lösung

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

- 5 cos (x) + 6 cos^{3} (x)

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

(- sin (2 x) \cdot 2) sin (x) + cos (x) cos (2 x) : - 5 cos (x) + 6 cos^{3} (x)

= - 5 cos (x) + 6 cos^{3} (x)

\int t^{5} - 7 t d t

\frac{\partial}{\partial x} (2 x^{2} + 4 y^{2} + 1)

\frac{d}{d x} (2^{x^{3} + 3 x})

tan (t) y^{^{'}} - y = 1

\int x^{2} x^{2} - 9 d x