MATH 151 Lecture Notes - Lecture 8: Chain Rule, Power Rule, Product Rule

• School: Simon Fraser University
• Department: Mathematics
• Course: MATH 151
• Professor: Stephen Choi

Document Summary

The chain rule is used to compute the derivative of a composition functions of f and g. let f (x) and g(x) be two differentiable functions so that f (x) and g (x) is given. Let h(x) be the composition function of f and g, that is, h(x) := (f g)(x) = f (g(x)). If h(x) = f (g(x)) (f g)(x), then the derivative of h(x) is given by h (x) = f (g(x)) g (x). In particular, if f (x) = xr is a power function, then h(x) = f (g(x)) = g(x)r. then by using. Chain rule, we have because f (x) = rxr 1. Hence we have h (x) = f (g(x)) g (x) = rg(x)r 1g (x) If then h(x) = f (x)r h (x) = rf (x)r 1f (x). Solution: let f (x) = x2012 and g(x) = 3x + 1.