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Lesson Lesson Implicit Differentiation Implicit Differentiation Implicit Function - is a function of the form R(X 1,..., Xn) = 0 Simple power Rule [x4 ] = 4x3 Example: f ( x, y ) = 0 g(x, y) = 0 u(x, y) = 0 Chain Rule Explicit Function -solving for y of an implicit f ( x, y ) = c function Implicit Function Example: y = f(x) y = g(x) Finding the first derivative of y wrt x If ( x, y) = 0 y = u(X) where: f, g, u = use to denote a function Determine y' (dy/dx) (x, y) = notation used to designate an ordered pair x = independent variable y = dependent variable Lesson Answer w/ solu Implicit Differentiation Homework GUIDELINES FOR IMPLICIT DIFFERENTIATION 1. ylnx - xlny =4, y' I. Differentiate both sides of the equation with respect to x 2. In(x2 + y2 )= 2 arctan ~, y' x ' 2. Collect all terms involving dy/dx on the left side of the equation and move all other terms to the right side of the equation. 3. In 3. Factor dy/dx out of the left side of the equation. 3x +1 X 4. Solve for dyldx