1. M ATHEMATICS WITH CALCULUS MAC 301 Course information Intro to Differentiation Review of year 12 skills Assignment 1.

2. D IFFERENTIATION BY S IGHT Function f(x)=ax n y= ax n Differentation Derivative/ derived function/ gradient function f ’(x)=nax n-1 dy/dx=nax n-1 To differentiate is to find the equation of the gradient function of any curve. Gradients describe the instantaneous rate of change The process of finding the derivative is called differentiation. Functions that can be differentiated are said to be differentiable.

3. D IFFERENTIATION R EVIEW 1. Powers of x y = x 3 y = x 2. Coefficientsy = 4πx 3 3. Constant termsy=5 4. Multiple terms y = x 10 -7x+5 5. Productsy=x 2 (2x 7 -6) 6. Quotients 7. Negative indices y = 3/x 7 8. Surds/ fractional indices NB: The convention is to give answers in the same form as the question.

4. Exercise 3.1C A1 (page 15) Differentiate the following functions: 2 3 4 1

5. 5 6 7 8 9 10

6. 1 Differentiate x 11 11 ─ 1 =10

7. 2 Differentiate x 3 ─ 9 3 3 ─ 1 = 2

8. 3 Differentiate x 2 + x + 1 2 1 

9. 4 Differentiate

10. 5 Differentiate

11. 6 Differentiate Write in index form:

12. 7 Differentiate Expand Simplify

13. 8Differentiate Expand Simplify

14. 9 Differentiate Divide through by (Multiply each term in the numerator by )

15. 10 Differentiate Divide through by (Same as multiplying by )