Homework SourseCalculate the derivative of 3x4 using both the definition of
Calculate the derivative of 3x-4 using both the definition of the derivative, and the Product rule. What is the derivative and what are the differences in these two procedures? If you think one might be better or not, explain why it is. In general, which is preferable, using the definition or using the derivative rules? Why?
Solution
Definition:
f(x + dx) = 3(x + dx) -4
f(x) = 3x +4
(lim dx--->0) f(x+dx) - f(x) / dx = 3dx /dx = 3
product rule:
d(3x-4)/dx = 3dx/dx = 3
usually general or definition is preferred.
