calculus - Derivative Of a function with respect to a different variable.

Today in a standard calculus course in high school,i notice that our sir wrote :
$$\frac{d}{dx} \cos(2t)=\frac{d}{dt}(\cos2t).\frac{dx}{dt}$$
But i am supposed to write as :
say $u=\cos(2t)$
Then $$\frac{du}{dx}=\frac{d}{dt}(\cos2t).\frac{dt}{dx}$$

That's what the chain rule says :
Please explain which of these is right and explain.