MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties
Problem
Let f(x)=cscx for all x in the domain of csc.
(a) Express f(x) as the reciprocal of a single elementary trigonometric function.
(b) Differentiate f(x) with respect to x and write the derivative using only sinx and cosx.
(c) Demonstrate algebraically that the derivative found in part (b) simplifies to −cscxcotx. Provide a clear sequence of algebraic steps leading to the final form.