Sections 3.1 and 3.2

Main Points: Sections 3.1 and 3.2 begin to introduce the derivative and the many rules for finding the derivative from a given equation. In the first section, the book states that the derivative of a constant, k, always equals zero. It then explains that the derivative of a linear function, mx + b, equals m since the derivative of a function is the slope. Also, if a function is multiplied by a certain number, say x^2 to 3x^2, then the derivative of the second function is simply the derivative of the first times the number it is multiplied by. Furthermore, derivatives of the sums or differences of two functions are simply the d/dx of function 1 +/- d/dx of function 2. Finally in section 3.1, the power rule is explained as d/dx [x^n]= nx^(n-1). In 3.2, the derivative of e is explained. Simply put, the derivative of e^x = e^x. Also, the exponential rule is stated as d/dx (a^x)= (ln a) * a^x. Finally, d/dx of ln x = 1/x. The graph of the function ln x is shown next to its derivative in order to show the differences and similarities between the two.

Challenges: In section 3.2, I found it very confusing the way the written explanation of a d/dx (a^x). However, once I studied the formula, I found it much less confusing.

Reflections: In calculus last year, we spent much time on derivatives. I found section 3.1 to be very easy, but section 3.2 was a much needed review for me. I always seemed to have trouble with the e^x and ln x derivative rules, but I now have a much better grasp on the situation.