MA110 Study Guide - Midterm Guide: Implicit Function, Quotient Rule, Maxima And Minima
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In this case, we use the method of implicit differentiation: Laurier sos: students offering support: differentiate both sides of the equation with respect to x, solve the resulting equation for. Example 1: find the derivative of the equation , then find the equation of the tangent line at the point (1,2). Step 1: differentiate both sides w. r. t x: side . Substituting in the point (1,2), we find that the slope of the tangent line at this point is: Substituting this slope and the point (1,2) into the equation , we find that and so the equation of the tangent line at (1,2) is. When taking the derivative of complicated functions involving products, quotients, or powers, it can often make things a lot easier if we take logarithms of both sides of the equation and use the laws of logarithms to simplify. Now, take the derivative of both sides (using implicit differentiation):
