Chapter 6
Exponential and Logarithmic
Functions and Tangent Lines
A
fter becoming familiar with the derivative techniques of the power, product, quotient,
and chain rules, you simply need to know basic formulas for different functions. In this
chapter, you see the derivative formulas for exponential and logarithmic functions. Knowing
the derivative formulas for logarithmic functions also makes it possible to use logarithmic
differentiation to find derivatives.
In many examples and applications, finding either the tangent line or the normal line to a
function at a point is desirable. This chapter arms you with all the derivative techniques, so
you’ll be in a position to find tangent lines and normal lines for many functions.
The Problems You’ll Work On
In this chapter, you do the following types of problems:
✓ Finding derivatives of exponential and logarithmic functions with a variety of bases
✓ Using logarithmic differentiation to find a derivative
✓ Finding the tangent line or normal line at a point
What to Watch Out For
Although you’re practicing basic formulas for exponential and logarithmic functions, you
still use the product rule, quotient rule, and chain rule as before. Here are some tips for
solving these problems:
✓ Using logarithmic differentiation requires being familiar with the properties of
logarithms, so make sure you can expand expressions containing logarithms.
✓ If you see an exponent involving something other than just the variable x, you likely
need to use the chain rule to find the derivative.
✓ The tangent line and normal line are perpendicular to each other, so the slopes of
these lines are opposite reciprocals.