Author:
Jim Fowler
Subject:
Calculus
Material Type:
Module
Level:
College / Upper Division
Provider:
Ohio Open Ed Collaborative
Tags:
  • Implict Differentiation
  • License:
    Creative Commons Attribution Non-Commercial
    Language:
    English
    Media Formats:
    eBook, Interactive

    Implicit differentiation modules

    Overview

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

    • Implicitly differentiate expression.
    • Find the equation of the tangent line for curves that are not plots of functions.
    • Understand how changing the variable changes how we take the derivative.
    • Understand the derivatives of functions that are not defined explicitly in terms of an independent variable .
    • Explain the formula for the derivative of the natural log function.
    • Calculate derivatives of logs in any base.
    • Calculate the derivative of an exponential function, axax, where a>0a>0.

    Standard form

    Ximera Module

    Two young mathematicians discuss the standard form of a line.

    Implicit differentiation

    Ximera Module

    In this section we differentiate equations that contain more than one variable on one side.

    Derivatives of inverse exponential functions

    Ximera Module

    We derive the derivatives of inverse exponential functions using implicit differentiation.

    Derivatives of inverse trigonometric functions

    Ximera Module

    We derive the derivatives of inverse trigonometric functions using implicit differentiation.

    The Inverse Function Theorem

    Ximera Module

    We see the theoretical underpinning of finding the derivative of an inverse function at a point.