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The Chain rule is given by: d[f(g(x))]/dx = f'(g(x)).g'(x)
In this class, we see the chain rule applied in three ways to get the following:
a) d/dx[u(x)n] = n(u(x))n-1u'(x)
b) d/dx[eu(x)] = u'(x)eu(x)
c) d/dx [ln(u(X))] = u'(x)/u(x)
1. Give an example of each of the three formulas above.
2. Explain how each one follows from the general chain rule. What is f(x) and what is g(x) in each of the formulas?
a motorboat can contain a constant speed of 38 mph relative to the water. the boat makes a trip upstream to a certain point in 42 minutes; the return trip is 34 minutes. what is the current?
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seating capacity of six is to be used by six employees who have formed a car pool. If only four of these employees can drive, how many possible seating arrangements are there for the group?
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