** 18.T Exponential and logarithmic functions and their derivatives **

** Reference: **
Stewart 6.2, 6.3, 6.4 (or review the
quick treatment from last semester
and then read 6.2*, 6.3*, 6.4* for a different approach)

** Keywords: ** Exponential functions, logarithms, logarithmic
functions, natural logarithms, the base of natural logarithms,
*e*,
logarithmic differentiation

** Learning Objectives: ** The student will be able to:

- Compute the derivatives of the functions
*f(x) = e*and^{x}*f(x) = e*, where^{u}*u*is a function of*x* - Compute the derivatives of the functions
*f(x)*= ln*x*,*f(x)*= log, and_{a}x*f(x)*= ln*u*, where*u*is a function of*x* - Evaluate simple integrals involving these functions,
and the integral of
*x*^{-1} - Use logarithmic differentiation

** 18.R Exponential growth and decay
problems;
Inverse trigonometric functions** (<--READ ME)

** Reference: ** Stewart 6.5, 6.6

** Keywords: ** Exponential growth, exponential decay, half-life,
Newton's law of cooling, continuous compounding of interest, first-order
chemical reaction, inverse trig functions, arcsin, arccos, arctan, derivatives
of these functions

** Learning Objectives: ** The student will be able to:

- Solve the differential equation
*dy/dt = ky*, and interpret the solution in terms of exponential growth (*k*> 0) or exponential decay (*k*< 0) - Recognize and solve common problems of the form
*dy/dt = ky*, such as radioactive decay, bacterial growth, Newton's law of cooling, continuously compounded interest, and first-order chemical reactions - Define and sketch the graphs of the the inverse trig functions arcsin, arccos, arctan
- Compute the derivatives of the above functions
- Use inverse trig functions in applications
- Recognize and evaluate integrals that involve inverse trig functions