Math 195 - Chapter 3

Back to John Weber's MAT195 Page
Back to MAT195 Assignments Page
Back to john-weber.com

Graph Paper with 2mm x 2mm divisions: pdf document (3 KB)
Graph Paper with 5mm x 5mm divisions: pdf document (2 KB)
(To save: right-click on link, select 'Save Target As...', select appropriate folder and click on Save)

Section 3.1 – Derivatives of Polynomials and Exponential Functions
- Read pp. 181 – 188
- online resources:
  1. Derivatives of Cubic Functions - http://www.ies.co.jp/math/products/calc/applets/bib3ji/bib3ji.html
    This site provides a java applet that shows (not proves) that the derivative of a cubic polynomial is a quadratic polynomial.
  2. Exploration: Exponential Functions and Their Derivatives - http://cs.jsu.edu/mcis/faculty/leathrum/Mathlets/explore1.html
    This exploration uses a small sample of the applets in the Mathlets package together to explore exponential functions and their derivatives in depth.
  3. Differentiating Sums of Functions - http://www.ugrad.math.ubc.ca/coursedoc/math100/notes/derivative/deriv-sums.html
    This site provides a proof of the sum and constant rules of differentiation.
  4. Power Rule, Chain Rule, & Product Rule - http://school.discovery.com/homeworkhelp/webmath/diff.html
    This site provides a solver that steps you through the power rule.
Section 3.2 – The Product and Quotient Rules
- Read pp. 190 – 194
- online resources:
  1. Product Rule Of Differentiation - http://www.netsoc.tcd.ie/~jgilbert/maths_site/applets/differentiation/product_rule_of_differentiation_.html
    This site provides a java applet that allows you to enter sample values for U and V and it will then take you through The Product Rule of differentiation, step by step.
  2. Quotient Rule - http://www.netsoc.tcd.ie/~jgilbert/maths_site/applets/differentiation/quotient_rule.html
    This site provides a java applet that allows you to enter sample values for U and V and it will then take you through The Quotient Rule of differentiation.
  3. Product and Quotient Rules - http://www.langara.bc.ca/mathstats/resource/onWeb/calculus/derivatives/computation/productrule.htm
    This site provides a proof of the sum and constant rules of differentiation.
  4. Quotient Rule - http://school.discovery.com/homeworkhelp/webmath/quorule.html
    This site provides a solver that steps you through the quotient rule.
  5. Power Rule, Chain Rule, & Product Rule - http://school.discovery.com/homeworkhelp/webmath/diff.html
    This site provides a solver that steps you through the product rule.
Section 3.3 – Rates of Change in the Natural and Social Sciences
- Read pp. 196 – 205
- online resources:
  1. links will be coming soon.
Section 3.4 – Derivatives of Trigonometric Functions
- Read pp. 208 – 213
- online resources:
  1. The Derivative of the Sine - http://www.ies.co.jp/math/products/calc/applets/difsin2/difsin2.html
    This site provides a java applet that demonstrates the derivative of the sine function.
  2. Derivatives of Trigonometric functions - http://www.ugrad.math.ubc.ca/coursedoc/math100/notes/derivative/trig2.html
    This site provides a discussion of the derivatives of trig functions.
  3. Power Rule, Chain Rule, & Product Rule - http://school.discovery.com/homeworkhelp/webmath/diff.html
    This site provides a solver that steps you through the product rule that includes trig functions.
Section 3.5 – The Chain Rule
- Read pp. 215 – 221
- online resources:
  1. Function Composition for Chain Rule - http://www.slu.edu/classes/maymk/Applets/FunctionCompositionCalc.html
    This site provides a java applet that graphically demonstrates the chain rule.
  2. Power Rule, Chain Rule, & Product Rule - http://school.discovery.com/homeworkhelp/webmath/diff.html
    This site provides a solver that steps you through the chain rule.
Section 3.6 – Implicit Differentiation
- Read pp. 224 – 230
- online resources:
  1. Implicit Differentiation I - http://www.ugrad.math.ubc.ca/coursedoc/math100/notes/derivative/implicit.html
    This site provides a java applet and a discussion on implicit differentiation.
  2. Implicit Differentiation II - http://www.netsoc.tcd.ie/~jgilbert/maths_site/applets/differentiation/implicit_differentiation.html
    This site provides a java applet that finds the derivative of axⁿ + bxy + cy^m = d.
  3. Inverse Trigonometric Functions - http://www.ugrad.math.ubc.ca/coursedoc/math100/notes/zoo/invtrig.html
    This site provides a java applet and a discussion on the differentiation of inverse trig functions.
Section 3.7 – Higher Derivatives
- Read pp. 233 – 237
- online resources:
  1. Derivative Applet - http://www.ma.utexas.edu/cgi-pub/kawasaki/plain/derivatives/2.html
    This site provides a java applet which finds the derivatives of a given function f(x) up to degree four, and graphs f(x), f'(x) and f''(x).
  2. Taylor Polynomial Approximation - http://www.slu.edu/classes/maymk/ApproxPoly/ApproxPoly.html
    This site provides a java applet that is designed for the exploration of approximation of functions by Taylor polynomials.
  3. Taylor Polynomial Applet - http://www.math.jhu.edu/~jrm/vander/stable/TPTest.html
    This site provides a java applet that is designed for the exploration of approximation of functions by Taylor polynomials.
  4. Derivative Calculator - http://cs.jsu.edu/mcis/faculty/leathrum/Mathlets/derivcalc.html
    This site provides a java applet that calculates the derivative of an expression specified using a simple expression syntax.
Section 3.8 – Derivatives of Logarithmic Functions
- Read pp. 240 – 245
- online resources:
  1. Derivative of Exponential and Logarithmic Functions - http://www.ies.co.jp/math/java/calc/e_diff/e_diff.html
    This site provides a java applet to better understand the derivative of exp(x) and ln(x). (NOTE: if you are prompted to install a component, CLICK CANCEL).
  2. Exponentials and Logarithms - http://www.karlscalculus.org/calc6_2.html
    This site provides a discussion of the derivation of the derivative of the logarithm function.
Section 3.10 – Related Rates
- Read pp. 253 – 256
- online resources:
  1. Related Rates Applications - http://www.nadn.navy.mil/MathDept/cdp/relatedrates/Application.html
    This site provides a discussion of related rates applications and a link to a java-based lab.

Back to John Weber's MAT195 Page
Back to MAT195 Assignments Page
Back to john-weber.com