Unit 2: Differentiation: Definition and Fundamental Properties

Use the limit definition of the derivative to answer the following.

Let [math] where [math] and [math] are constants.

Differentiate each function. Show all steps.

Let [math].

A rocket's altitude in meters is modeled by [math] for [math] seconds.

Use logarithmic differentiation or appropriate rules to find each derivative.

Find [math] for each function.

The table below gives values of a differentiable function [math] and its derivative [math].

Let [math] on the interval [math].

Let [math]. Note that [math] is one-to-one.