MATH 180 Study Guide - Final Guide: Quotient Rule, Asymptote, Intermediate Value Theorem
Document Summary
Problem 1 solution: compute the derivatives of the following functions: (a) y = x. 1 + x3 (b) y = sin( x + 1) (c) y = x psin(x) + 1. Solution: (a) the derivative may be computed using the quotient rule. dy dx dy dx dy dx (1 + x3)(x) . (x)(1 + x3) (1 + x3)2 (1 + x3)(1) (x)(3x2) (1 + x3)2. 1 2x3 (1 + x3)2 (b) the derivative calculation here requires the chain rule. dy dx dy dx. = cos( x + 1) d dx (cid:0) x + 1(cid:1) 2 x (c) both the product and chain rules are necessary to compute this derivative. dy dx dy dx dy dx. + (x) psin(x) + 1 (sin(x) + 1) + 1 psin(x) + 1 d dx. 2psin(x) + 1 cos(x) + psin(x) + 1. Problem 2 solution: find the equation of the tangent line to y = x + 1 at x = 3.
