Introduction to the idea of a derivative as instantaneous rate of change or the slope of the tangent line. The Definition of the Derivative In the first section of the Limits chapter we saw that the computation of the slope of a tangent line the instantaneous rate of change of a function and the instantaneous velocity of an object at x a x a all required us to compute the following limit. Can derivatives be extraordinarily complex.
In other words the slope at x is 2x.
We write dx instead of Dx heads towards 0. Derivatives are fundamental to the solution of problems in calculus and differential equations. We write dx instead of Dx heads towards 0. Lim xa f x f a x a lim x a.