STA2203
CHAPTER 1: DIFFERENTIATION: BASIC CONCEPTS
1.1 The Derivative
Calculus is the mathematics of change, and the primary tool for studying change
is a procedure called differentiation.
Rates of Change and slope
y = mx + c
y
(0, c)
x
x
y
m
x
=
y 2 y1
x

CHAPTER 2: INTEGRATION
2.1 The General Integration or Antiderivative of a Function
Rules for Integrating Common Functions
The constant rule:
k and C are constant
kdx kx C
The power rule:
n
x dx
The logarithmic rule:
x n 1
C
n 1
1
x dx ln x C
The exponent

Tutorial 1
1.
Compute the derivative of the given function and find the slope of the line that is tangent
to its graph for the specified value x. Hence, find the relevant equation of the tangent line for
the specified value of x = c.
(a) f(x) = 5x -3; x =