This final unit in the study of calculus AB begins with a discussion of inverse
functions and the algebraic and geometric relationship between a function *f*
and its inverse *f*^{-1}. The geometric property of *f*^{-1} as a reflection of
*f* across the line *y* = *x* is used to develop a formula for finding the
derivative of *f*^{-1} from *f*.

Next is an introduction to the function *f* (*x*) = *e*^{x} and its inverse *f* (*x*) = *ln*(*x*).
After a brief discussion of the properties of these functions, we see that the
derivative of *f* (*x*) = *e*^{x} is in fact *e*^{x} itself, and that the derivative of
*f* (*x*) = *ln*(*x*) is the function , which is the only power function
that could not be integrated by reversing the power rule. The derivatives of
*e*^{x} and *ln*(*x*) are used to develop methods to differentiate functions where
*x* is in the exponent. Finally, the general form of functions that exhibit
exponential growth or decay is presented.

Take a Study Break!