I've attached Sections 2.2 and 2.3 of a calculus book by Keisler.
See especially pages 59 and 69 of the book,
which are pages 7 and 17 of the attached file 03p.pdf.
There you will find many exercises
asking you to find a differential or a derivative.
Keisler's book may be freely copied for non-commercial purposes:
http://www.math.wisc.edu/~keisler/calc.html
The book uses a fancy word, "infinitesimal."
The author's intended meaning is "infinitely small,"
but if you don't like that idea, just read "infinitesimal"
as "small enough to make all the errors in the
approximations I'm currently using also small."
Sections 2.2 and 2.3 also mention tangent lines.
We haven't covered these in class yet,
but we will on Day 6 (Feb. 9).
P.S. For your reference:
Basic rules, assuming a is a constant:
d(a) = 0
d(a * u) = a * du
d(u + v) = du + dv
d(u * v) = u * dv + v * du
d(u^a) = a * u^(a-1)
Some useful rules that can be proven from the basics,
assuming a, b, and c are constants:
d(u^2) = 2 * u * du
d(u^3) = 3 * u^2 * du
d(u^(1/2)) = du / (2 * u^(1/2))
If w = u * v, then
dw / w = du / u + dv / v.
If w = u^a * v^b, then
dw / w = a * du / u + b * dv / v.
If w = x^a * y^b * z^c, then
dw / w = a * dx / x + b * dy / y + c * dz / z.
More useful rules that we will cover in future classes
(still assuming a is a constant):
d(1 / v) = -dv / (v^2)
d(u / v) = (v * du - u * dv) / (v^2)
d(ln(u)) = du / u
d(e^u) = e^u * du
d(a^u) = a^u * ln(a) * du
A copy of this email and attachment are archived at:
http://dkmj.org/2cd875e4f5f6ffc05f86be274af19af9/notes/03.txt
http://dkmj.org/2cd875e4f5f6ffc05f86be274af19af9/notes/03p.pdf