MTH 161 Lecture Notes - Lecture 12: Trigonometric Functions

• School: University of Miami
• Department: Mathematics
• Course: MTH 161
• Professor: Staff

Document Summary

Provide a generalization to each of the key terms listed in this section. The chain rule occurs when you have both f and g are di erentiable, which means that (f g) (x) = f (g (x)), which can be written by the following formula: d dx. [f (g (x))] = f (g (x)) g (x) Also, if you use substitution and let both y = f (u) and u = g(x), then the following can be expressed in the same way: dy dx. = f (g (x)) g (x) The derivative can be written, with limits, as the following: d dx. [f (g (x))] = lim h 0(cid:20) f (g (x + h)) f (g (x)) h (cid:21) 1 f (x) = 2x2 + 3x + 4 g (x) = 2e3x f (g (x)) = 8e6x + 6e3x + 4 f (g (x))