Derivatives and Antiderivatives

Abstract

Mathematical functions come in all sorts of shapes and sizes. Sometimes they are described explicitly where y equals some function of its independent variable(s), such as

$$y=x\sin x $$

or implicitly where y, and its independent variable(s) are part of an equation, such as

$$x^2+y^2=10. $$

A function may reference other functions, such as

$$y=\sin\bigl(\cos^2x\bigr) $$

or

$$y=x^{\sin x}. $$

There is no limit to the way functions can be combined, which makes it impossible to cover every eventuality. Nevertheless, in this chapter we explore some useful combinations that prepare us for any future surprises.