why do we use to differentiate a quantity?dy/dt represents rate change but how do it represent slope

Question

my problem is from smaller classes i have been taught dy/dt is a rate changing operator but how is this possible that a rate changing operator changes the unit step function to a impulse function

Answer 1

dy/dx=rate y chaenj / rate x chaenj =slope

its the tangent, from a triangel (trig)