derivative of cos(2xsin(3x))

Lösung

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

- 2 sin (2 x) sin (3 x) + 3 cos (3 x) cos (2 x)

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = cos (2 x), g = sin (3 x)

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

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

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

= (- sin (2 x) \cdot 2) sin (3 x) + cos (3 x) \cdot 3 cos (2 x)

Vereinfache

= - 2 sin (2 x) sin (3 x) + 3 cos (3 x) cos (2 x)

\int (7 x^{6} - \frac{6}{x ^{6}}) d x

\int x^{2} - 3 x + 8 d x

s l o p e in t erce pt (- 7, - 6), (10, 8)

t a y l or (3 x - 10)^{\frac{4}{3}}

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