## Week 18

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) = ex and f(x) = eu, where u is a function of x
• Compute the derivatives of the functions f(x) = ln x, f(x) = loga x, and 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