Author:
Ohio Open Ed Collaborative
Subject:
Calculus
Material Type:
Module
Provider:
Ohio Open Ed Collaborative
Tags:
  • Cac077
  • Rules of Differentiation
  • License:
    Creative Commons Attribution Non-Commercial
    Language:
    English
    Media Formats:
    eBook, Interactive

    Rules of differentiation modules

    Overview

    After completing this section, students should be able to do the following.

    • Use the definition of the derivative to develop shortcut rules to find the derivatives of constants and constant multiples.
    • Use the definition of the derivative to develop shortcut rules to find the derivatives of powers of xx.
    • Use the definition of the derivative to develop shortcut rules to find the derivatives of sums and differences of functions.
    • Compute the derivative of polynomials.
    • Recognize different notation for the derivative.
    • State the derivative of the natural exponential function.
    • State the derivative of the sine function.

    Patterns in derivatives

    Ximera Module

    Two young mathematicians think about ``short cuts'' for differentiation.

    Basic rules of differentiation

    Ximera Module

    We derive the constant rule, power rule, and sum rule.

    The derivative of the natural exponential function

    Ximera Module

    We derive the derivative of the natural exponential function.

    The derivative of sine