I don't quite understand how to derive from first principals.
I understand that it is a point x+h - x for delta x and how h is delta y but i still have trouble working through them. i have tried googleing a few examples but the formatting hurts my brain.
Would anyone mind going through an example for me of 3x^2+4x-6
I believe it starts at (3(x+h)^2+4(x+h)-6)-(3x^2+4x-6) all over h lim as h -> 0 but would someone mind taking me step by step through it?
Hello, Swiftspice!
I'll show you the way I taught it to my Calculus classes.
Differentiate from first principles.
Definition: .
I break this up into four steps:
[1] Find . . . . Replace with . . . and simplify.
[2] Subtract . . . Subtract the original function . . . and simplify.
[3] Divide by . . . . Factor and reduce.
[4] Let . . . . . .Let . . . and simplify.
Here we go!
. . . . . . . . . . . . . .
. . . . . . . . . . . . . .
. . . . . . . . . . . . . .
Therefore: .