# Definition of the Derivative & Questions

Please see the attached file for the fully formatted problems.

Key points:

The derivative of at is the instantaneous rate of change of and it is denoted by .

If we let , we obtain an equivalent formula

that is at times more convenient to use in problems. A function for which the exists is called differentiable at . A function is differentiable on an interval if it is differentiable at each number in that interval.

Given we define a new function . This is the derivative function. The derivative describes how quickly is changing. Other notations for the derivative function are (where ), , .

Interact (use left and right arrow keys) with this (quicktime) animation that illustrates a function and its derivative. Before you play it try to sketch on a piece of paper.

The derivative of the derivative of is denoted by: or sometimes by .

1. Use the definition of derivative to calculate where .

2. Use the definition of derivative to calculate where .

3. Use the definition of derivative to calculate where .

4. Use the definition of derivative to find .

https://brainmass.com/math/derivatives/definition-derivative-questions-148848

#### Solution Preview

Please see the attached file for the complete solution.

Thanks for using BrainMass.

Page 1

Please help & please show step-by-step, thx, appreciate it.

Below are notes my instructor gave for this assignment that are relative and important to how we do the problems there are 4 problems & a total of two pages. Thank you

Key points:

The derivative of at ...

#### Solution Summary

The definition of the derivative is applied to four simple derivative questions. The solution is detailed and well presented.