MATH-M 211 Lecture Notes - Lecture 6: Quotient Rule, Polynomial, Product Rule
Document Summary
Section 2. 3 notes- product and quotient rules and higher-order derivatives. Note: no negative exponents, no complex fractions, combine like terms, always try to simplify original function. Derivative of sum of functions = sum of derivatives o. Derivative of products product of derivatives o. Product rule: proven by definition of derivative. Add in extra term that cancels itself out to get the problem going somewhere . Definition of derivative : (first)(deriv. second) + (second)(deriv. first) Derivative properties o o o o o o. Ex. y = (5x2 6)(3x + 7: y" = (5x2 6)(3) + (3x + 7)(10x, y" = 15x2 18 + 30x2 + 70x, y" = 45x2 + 70x 18. Ex. y = x2sin x: y" = (x2)(cos x) + (sin x)(2x, y" = x2cos x + 2xsin x. = (2x + 3)(x-1: y" = (2x + 3)(-x-2) + (x-1)(2, y" , y" = Derivative of quotient quotient of derivatives o. Quotient rule- given that g(x) 0.
