The Chain rule is the absolute most important rule in all of differentiation, it is the oly rule that is ALWAYS applied, you have been applying it, u just didn't notice. $$\frac{d}{dx} f(g(x)) = f'(g(x)) \cdot g'(x)$$ so for example: $$\frac{d}{dx} \sin(2x)$$ $$f(x) = \sin x \implies f'(x) = \cos x \implies f'(g(x)) = \cos(2x)$$ $$g(x) = 2x \implies g'(x) = 2$$ Thus: $$\frac{d}{dx} \sin(2x) = f'(g(x)) \cdot g'(x) = \cos(2x) \cdot 2$$