I wish you a teacher like this.
Morris Klein in Calculus: An Intuitive Approach:
In many instances I have deliberately made false starts so as to have the student realize that correct methods and correct proofs are almost always preceded by groping and to have students appreciate why we finally take one course rather than another. I wish to dispel the impression that good mathematicians are able to proceed directly to the right conclusion because strict logic or a God-given insight guides them.
If you sometimes wonder why we put ourselves through all this hocus-pocus, this guy will walk you through the answer.
I know. You're overwhelmed. Someone tries to help but he gives you even more to read, even more to learn.
Trust him. Go the long way around. The shortcut only gets you lost faster. Was the Donner Pass a shortcut to California, or to a long winter of cannibalism? The long way gets you there quicker.
You learn best when you're playing, and 3Blue1Brown on YouTube (Grant Sanderson) plays with some beautiful pictures of ideas that were never beautiful before.
Dawdle a moment over some of these titles from 3Blue1Brown:
Tattoos on Math After a friend of mine got a tattoo with a representation of the cosecant function, it got me thinking ...
You'll never again see sin or cos or tan without seeing them flow from one to another this way.
No, calculus isn't about the area under a curve, that's just everyone's favorite illustration or analogy for showing something else. This might be your new favorite.
Before you give up on Taylor Series, watch them whip around like caught snakes here:
What a break, eh, if you could turn all these functions into polynomials? You already know all about polynomials.
You'll come away with a feel for more than Taylor Series, and more than you knew to ask for.
Which would you rather bring to mind when you hear "chain rule"?
I could never learn anything I hated, but I could learn nearly anything if I could find my own reasons to care. I needed that first.
Find your own reasons to want calculus. Not for the degree. Not for your advisor. Not for the teacher. Not for a pushy parent. Not even for friends or enemies you want to impress. Your own reasons, for you. If no one would ever know, you would still want to know.
Teachers like Morris Kline and Grant Sanderson teach you to play. Those were always my best teachers, the ones who taught me their curiosity and love of the subject. Nothing moves until you care,and nothing moves where you stop caring.
Morris Kline is right. After this you'll know if you're off by a thousand percent. You'll feel it.