Readings

NEUHAUSER 3rd ed  primary text

Sec. 4.71, p. 183-188, derivatives of inverse functions

Sec. 4.7.2&3, p. 188-192, logarithm derivative and logarithmetic derivatives

Sec. 4.4.4, p. 169-172, higher derivatives

Sec. 4.4.2, p. 165-167, implicit differentiation

Sec. 5.7, p. 262-266, Newton-Raphson's Method

see example 4, p. 187 , for derivatives of inverse trig functions
(trig functions are sometimes referred to as circular functions)
skim sec. 4.4.3, related rates; this is a common topic in calculus courses!
Newton_Raphson's method is sometimes called Newton's Method for finding roots,   
i.e. finding the value of x=xo such that y = f(xo) = 0 

NEUHAUSER 2nd ed

Sec. 4.7, p. 223-233, derivatives of inverse functions

Sec. 4.7.3, p. 231-233, logarithmetic derivatives

Sec. 4.4.4, p. 206-208, higher derivatives

Sec. 4.4.2, p. 200-203, implicit differentiation

Sec. 5.7, p. 318-325, Newton-Raphson's Method

in note above replace "example 4, p. 187" with "example 4, p. 228"