Chapter 3.06: Derivatives of Logarithmic Functions
2
5
6
12
15 (iterated logarithms pop up in math, probability, and computer science)
25
26
30 (iterated logarithms pop up in math, probability, and computer science)
34 (products of powers of x with logarithms pop up in computer science)
43
53 WEP
56 WEP

QA: 
i) graph ln(1+e^x) from x=-10 to 10
ii) sketch its derivative graph by hand.
iii) find the derivative using formulas, and graph it.
iv) what is the name of the function you got in part (iii)?

QB: as x goes to infinity,
i) describe how 1-exp(-x) behaves
ii) describe how its derivative behaves
iii) describe how ln(x) behaves
iv) describe how the derivative of ln(x) behaves
v) Can we say "If the derivative goes to zero, then the function
stays bounded" as x goes to infinity? Explain.

QC: The Rocket Equation
The velocity of a rocket t seconds after liftoff from earth
can be modeled by
v(t) = -g*t - v_e * ln( (m-rt)/m )
where
g = 9.8 m/s^2, the usual earth gravity value,
v_e = exhaust velocity, 3000 m/s (the e here isn't related to 2.71828...)
m = initial mass of the rocket+fuel: 30,000 kg
r = rate of using fuel = 160 kg/s
i) Find the acceleration function a(t) and graph it, t=0 to 60
ii) Find the jerk function j(t) = a'(t) and graph it, t=0 to 60
iii) optional: what happens as t approaches 187.5 ? Explain.
iv) major bonus points: buy such a rocket and bring it to class for
a demonstration.

Note: some of the problems we're doing above will appear again in
Calc II when we take integrals, which is like doing derivatives backwards.