Why is the chain rule applied to derivatives of trigonometric functions? I'm having trouble to understand why is the Chain rule applied to trigonometric functions, like:
$$\frac{d}{dx}\cos 2x=[2x]'*[\cos 2x]'=-2 \sin 2x$$
Why isn't it like in other variable derivatives? Like in:
$$ \frac{d}{dx} 3x^2=[3x^2]'=6x $$
Does it means it is the derivative of the trig function times the derivative of the angle?
Thanks once again.

A more appropriate example would be
$$\frac{d}{dx} (3x)^2=2(3x) \cdot (3x)' = 18x$$
