1. © Annie Patton Differentiation of Products Next Slide

2. © Annie Patton Aim of lesson To learn how to differentiate products. Next Slide

3. © Annie Patton What is a product? 2 x 3 20 X 46 x(x 2 + 3x) So it is two things multiplied together. Next Slide

4. © Annie Patton To get the derivative of a product For example (x + 2) (x 2 +3x) You could multiply it out x ( x 2 +3x) +2(x 2 +3x) = x 3 + 3x 2 + 2x 2 + 6x =x 3 + 5x 2 + 6x Next Slide Now for an easier method!!!

5. © Annie Patton To Differentiate y = (x + 2)(x 2 + 3x) Let u = x + 2 and v= x 2 + 3x Next Slide =3x 2 + 10x+6

6. © Annie Patton Product Rule Next Slide

7. © Annie Patton Why ? The derivative of y=(x 3 +3x)(x 2 +6) equals (x 3 +3x)(2x)+(x 2 +6)(3x 2 +3) u v Next Slide

8. © Annie Patton Differentiate y=(2x-5)(3x 2 +6) Let u equal(2x-5) and v equal (3x 2 +6). Use the formula Then So Next Slide Start clicking when you want to see the answer.

9. © Annie Patton Differentiate y=x 3 (cos x) Let u equal x 3 and v equal cos x. Use the formula Then So Next Slide Start clicking when you want to see the answer. Remember from First Principles. Also see tables.

10. © Annie Patton Proof of Product Rule by First Principles Next Slide Leaving Certificate 2000 Higher Level Paper 1 no 6(b)(i)

11. © Annie Patton Leaving Certificate 2006 Higher Level Paper 1 no 6(a) Next Slide Start clicking when you want to see the answer.

12. © Annie Patton Start clicking when you want to see the answer. Next Slide

13. © Annie Patton Next Slide

14. © Annie Patton Now differentiate the following exercises by the Product Rule Next Slide

15. © Annie Patton A link to VISUAL CALCULUS Next Slide Click to get more examples for the product rule, but ignore the ones with e in it.

16. © Annie Patton Product Rule