1. Section 2 – Derivatives and Antiderivatives
Chapter 15
Section 2 – Derivatives and Antiderivatives

2. What is a Derivative?
The derivative of a function is the equation for the SLOPE of a tangent line to the function at any given point.
To find the derivative of a function, we will go over some basic rules.

3. Derivative Rules
Constant Rule: The derivative of a constant function is zero. If f(x) = c, then f’(x) = 0.
Power Rule: If f(x) = xn , where n is a rational number, then f’(x) = nxn-1
Constant Multiple of a Power Rule: If f(x) = cxn , where c is a constant and n is a rational number, then f’(x)=cnxn-1

4. Find the Derivative of Each Function
EX 1: f(x) = x6
EX 2: f(x) = x2 – 4x + 2
EX 3: f(x) = 2x4 – 7x3 + 12x2 – 8x – 10
EX 4: f(x) = x3(x2 + 5)
EX 5: f(x) = (x2 + 4)2

5. Assignment (Part 1) Chapter 15, Section 2 (part 1)
p. 957 # 4 – 9 p. 958 #

6. Antiderivative Rules
Power Rule: If f(x) = xn , where n is a rational number other than -1, then the antiderivative F(x) = 1 𝑛+1 xn+1 + C
Constant Multiple of a Power Rule: If f(x) = kxn , where k is a constant and n is a rational number other than -1, then F(x)=k 1 𝑛+1 xn+1 + C
Sum and Difference Rule: If the antiderivatives of f(x) and g(x) are F(x) and G(x) respectivelty, then the antiderivative of f(x) ± g(x) is F(x) ± G(x)

7. Assignment (Part 2) Chapter 15, Section 2 (part 2)
p. 957 # 10-12, p. 958 #