Unit 3: Differentiation: Composite, Implicit, and Inverse Functions

Unit 3 extends your derivative toolkit to functions built from other functions. The chain rule is the star: differentiate the outside, keep the inside, multiply by the derivative of the inside, and learn to apply it from tables of values, not just formulas. You'll then use implicit differentiation to find slopes on curves that aren't functions, differentiate inverse functions with g'(a) = 1 / f'(g(a)), and learn the derivatives of the inverse trig functions. The unit wraps up with choosing the right procedure for a given derivative and finding higher-order derivatives, including second derivatives of implicitly defined curves. Write out each layer of a composite function before differentiating and most mistakes disappear.