This document contains a calculus review that includes: 1) Finding the derivatives of various functions such as x^2 + 3x - 5. 2) Using given information about functions f(x), g(x) and their derivatives at x = -5 to find the derivative of h(x) = f(x)/g(x) at that point. 3) Finding the equations of the tangent and normal lines to the graph of y = 3x^2 - x at x = -1. 4) Reviewing the rules for finding derivatives and working through several examples.

1. Calculus Review
Find the derivative
x2 + 3x –5
x
1. ƒ(x) =
2. ƒ(x) = (x2–5)3
3. ƒ(x) = (2x+3)2

2. Let’s Think!
Assume f(-5) = 0,
f’(-5)= -10, g(-5) =1,
g’(-5) =-1/5. Find h’(-
5) given h(x)
=f(x)/g(x)

3. Getting Warmed
Up! Find the equation of the
tangent to the graph of
y = 3x2 - x at x = - 1.
Find the equation of the
normal line to the graph of
y = 3x2 - x at x = - 1

4. Calculus
Objective
STW review all rules to
finding derivatives

5. Find the derivative
1
X – 2
1. ƒ(x) =

6. Find the derivative
–1
(X – 2)2
1. ƒ’(x) =

7. Find the derivative
2. ƒ(x) = 2(X2 – 1)3

8. Find the derivative
2. ƒ’(x) = 12x(x2 – 1)2

9. Find the derivative
3. ƒ(x) = √ 3 – 2x

10. Find the derivative
√ 3 – 2x
3. ƒ’(x) =
–1

11. Find the derivative
4. ƒ(x) = 2x3(x2 – 2x)

12. Find the derivative
4. ƒ’(x) = 10x4 – 16x3

13. Find the derivative
3
5. ƒ(x) = 2√ 2x2 – 3

14. Find the derivative
3( 2x2 – 3)2/3
5. ƒ’(x) =
8x

15. Find the
derivative
6. ƒ(x) = x√ 1–x2

16. Find the derivative
3x + 2
x – 1
7. ƒ(x) =