>>13864320depends on how deep you want to go into it.
if youre an engeneering math level person thant it surfice to view it as the instantaneos rate of change. which becomes very obvious from the definition via differencial quatient.
If youre physicist or mathematician lvl math person, the derivative has also other interpretations. For those though you dont only need trigonomoetry but rather differential geometry and algebraic topology. (search for "the derivative isnt what you think it is" on youtube). But the intermediate level between rate of change and co-homology would be the derivative as a linear approximation in a neighbourhood. You see what it means for a function to be differentiable (or smooth for that matter) is that it locally looks like a straight line (or plane/hyperplane).
But in the end it really depends on the context. For example from a group theoretical perspective the derivative is the generator of translations of a function (this becomes very important in eg quantum mechanics).