3 ms·
Do you have intuitive understanding of the derivative rules? For example: d/dx of x^3 = lim h->0 of ((x+h)^3 - x^3)/(h) = lim h->0 of (x^3 + 3hx^2 + 3xh^2 + h
by chongli 3y ago
Do you have intuitive understanding of the derivative rules? For example:
d/dx of x^3 = lim h->0 of ((x+h)^3 - x^3)/(h)
= lim h->0 of (x^3 + 3hx^2 + 3xh^2 + h^3 - x^3)/(h)
= lim h->0 of 3x^2 + 3xh + h^2
= 3x^2
So then if we started with (x^3)/3 the 3s would cancel and we’d get x^2. This tells us that the antiderivative of x^2 is (x^3)/3.
Or did you mean some other intuition? Such as why the fundamental theorem of calculus (that integration and differentiation are inverses of one another) is true?