Section 6.2—Substitution

Method of substitution:  The Chain Rule says, if h = g(u) and u = f(x), then h(x) = g(f(x)) and

h’(x) = g’(f(x)) f’(x).  So,

Examples:

Consequences of Substitution: If u = f(x), then du = f ’(x) dx and

General Power Rule                 

General Exponential Rule         

General Logarithmic Rule         

It might be worth memorizing

Practice