6.3. Differentiation and Integration of Logarithmic and Exponential Functions http://www.ck12.org
6.3 Differentiation and Integration of Logarith-
mic and Exponential Functions
Learning Objectives
A student will be able to:
- Understand and use the rules of differentiation of logarithmic and exponential functions.
- Understand and use the rules of integration of logarithmic and exponential functions.
In this section we will explore the derivatives of logarithmic and exponential functions. We will also see how the
derivative of a one-to-one function is related to its inverse.
The Derivative of a Logarithmic Function
Our goal at this point to find an expression for the derivative of the logarithmic functiony=logbx.Recall that the
exponential numbereis defined as
e=alim→ 0 ( 1 +a)^1 /a(where we have substitutedaforxfor convenience). From the definition of the derivative off(x)that you already
studied in Chapter 2,
f′(x) =hlim→ 0 f(x+hh)−f(x)=wlim→xf(ww)−−xf(x).We want to apply this definition to get the derivative to our logarithmic functiony=logbx.Using the definition of
the derivative and the rules of logarithms from the Lesson on Exponential and Logarithmic Functions,