Math 230 Weekly Activity 6 Learning Outcomes: Calculate the derivative of a function using the chain rule Calculate the derivative of an implicit function Given a composition of two functions y = f(g(x)). we can call f(x) the OUTSIDE function and g(x) the INSIDE function Example: y(x) = sin(x?) = f(9(x)) where f(x) = sin x (outside function) and g(x) = x (inside function). We know how to calculate the derivative of f(x) and g(x). Then the CHAIN RULE states that the derivative of the composite function y = f(g(x)) is y' = f' (9 (x) ) g' (x ) Example: f' (x) = cosx , g'(x) = 2x, y'(x) = cos(x?) 2x 1. Using the chain rule multiple times a) y = cos v3x2 + x -1 b) y = sin(sin(3x))