MAT 1330 Lecture Notes - Lecture 11: Quotient Rule

• School: University of Ottawa
• Department: Mathematics
• Course: MAT 1330
• Professor: Catalin Rada

Document Summary

F (g(x)) = y = e3x g = 3x and f = eg dy dx df dg dg dx. Find the derivative. y = ex2 outer derivative. Eg) y = (4x2 3x 2)13. Find the derivative. y = 13(4x2 3x 2)12(8x 3) outer derivative derivative from within. 1 (1 + ln x)2 f = 1 g and g = 1 + ln x. 1 x (or we could use the quotient rule) We can apply the chain rule over and over if we want since y(x) = f (g(h(x))) dy dx df dg dg dh dh dx. Eg) y = ln[(x2 + 2x)5 + 3]. Find the derivative. f = ln g g = h5 + 3 h = x2 + 2x y = 1 g 5h4 (2x + 2) (x2 + 2x)5 + 3 5(x2 + 2x)4 (2x + 2) = et ln 3 y = ln 3 et ln 3.