Give an example of each of the three formulas - explain how

Question

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)e^u(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?