Differential Calculus
Here we will learn about different aspects of differential calculus.
Table of Contents
- Definition of Derivative
- Visualization of Derivative
- Visualization of Derivative Part 2
- Special Functions
- Exponential Derivatives
- Derivative of Natural Log
- Derivative of Sine
- Derivative of Cosine
Visualization of Derivative
The below app shows four different functions, which you can switch by pushing "Switch Function". It also has two points, F and M, and you can move point M using the slider. You can also show the tangent and chords. [br][br]Play around with the app until you understand the buttons, and then answer the questions below.
[b]Step 1: [/b]We want to find the slope of the tangent line, which goes through point F on the function. Push "Show Tangent at F".[br][br][b]Step 2:[/b] We can easily find the slope between two points, if we have their coordinates. So, if we have a point M, we can draw a [b]chord[/b] through the two points, and find the slope. Push "Show Chord Through F and M".[br][br][b]Goal: [/b]Now, we want to [b]estimate[/b] the slope of the tangent line at F, using the chord through F and M.[br][br][b]Question 1: [/b] By moving point M, how can we make the chord through F and M close to the tangent line through F?[br][br][b]Question 2:[/b] Try your method for the remaining three functions, by pushing "Switch Function". Does your method still work?[br][br][b]Question 3: [/b] What happens if we move M to exactly F? Explain why.[br][br][b]Question 4: [/b]What idea have we learned about recently in math, that uses both your answers to question 2 and 3?[br]
Exponential Derivatives
Adjust the sliders, so that f(x)=f'(x). What is b at this point?