MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties
Problem
Consider h(x)=cot(kx), where k is a non-zero real constant.
(1) Express h(x) using only sin(kx) and cos(kx).
(2) Find h′(x) and simplify your answer completely in terms of cotangent or cosecant functions, as appropriate.
(3) For k=3, evaluate h′(6π) and state its exact value.