derivative of sin(6xcos(4x))

Lösung

\frac{d}{d x} (sin (6 x) cos (4 x))

6 cos (6 x) cos (4 x) - 4 sin (4 x) sin (6 x)

Schritte zur Lösung

\frac{d}{d x} (sin (6 x) cos (4 x))

Wende die Produktregel an:

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

f = sin (6 x), g = cos (4 x)

= \frac{d}{d x} (sin (6 x)) cos (4 x) + \frac{d}{d x} (cos (4 x)) sin (6 x)

\frac{d}{d x} (sin (6 x)) = cos (6 x) \cdot 6

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

= cos (6 x) \cdot 6 cos (4 x) + (- sin (4 x) \cdot 4) sin (6 x)

Vereinfache

= 6 cos (6 x) cos (4 x) - 4 sin (4 x) sin (6 x)

x^{4} + y^{3} x^{5} + 5 y^{^{'}} = 0

3 x^{2} y^{2} d x + 2 x^{3} y d y = 0

d er i v a t i v e f (x) = 2 - 4 x

a re a 4, \frac{e ^{x}}{5}, x = 0

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