"Derivatives" 11 posts

Here is the Khan Academy 3rd derivative video:

#### First and second derivative test

An Educational video on first and second derivatives:

#### Power rule example

Video on Determining derivatives using the power rule:

#### Numerically Approximating rate of change worksheet

A worksheet for derivative calculation:

#### Lab 3 Part I, Calculus I

Unity College, Carrie Diaz Eaton

Consider an environmental indicator which can be described by the following equation:

P(t)=et

where t is in years.

1. Sketch a graph of P(t) and from that, sketch what you expect P’(t) to look like.

2. Write an equation for P(t+∆t)

3. Try to calculate the derivative algebraically using the limit definition of derivative

4. Create a spreadsheet that calculates the derivative numerically at 21 different points of the graph:  t = 0, .5, 1, 1.5, … 10

(Hint: Create a table for with 21 rows (t = 0, .5, 1, 1.5, … 10) and 8 columns: t,P(t),  then for∆t=1 P(t+∆t), P/∆t=[P(t+∆t)-P(t)]/∆t, then for∆t=.1 P(t+∆t), P/∆t=[P(t+∆t)-P(t)]/∆t, and for∆t=.01 P(t+∆t), P/∆t=[P(t+∆t)-P(t)]/∆t.)

1. Results Graph a scatterplot of P(t) and your estimates of P’(t) based on the numerical work performed in #4.

2. Discussion Do the visual results based on visual, algebraic and/or numerical work agree?

3. Discussion Contrast the initial and long-term value of the instantaneous rate of change.

Discussion Suppose a different function was hypothesized for P(t), such as t^2 or e^(-t).  How would you modify your spreadsheet to approximate the graph of the derivative?

#### differntialbility and tangent line equation

Educational video on how to get a tangent line equation:

#### Proof: d/dx(sqrt(x)) | Taking derivatives | Differential Calculus | Khan Academy

This educational video is on Taking derivatives :

#### Calculus: Derivatives 2 | Taking derivatives | Differential Calculus | Khan Academy

Another video on more advanced derivatives:

#### Calculus: Derivatives 1 | Taking derivatives | Differential Calculus | Khan Academy

video on the basics of derivatives:

#### Derivative intuition module

This Khan Academy video is to help better understand the equation for a derivative determining the slope at any given time: