1. © Annie Patton Differentiation by First Principles Next Slide

2. © Annie Patton Aim of Lesson To learn, what is meant by differentiation by First Principles and to see how to do this in five steps. Next Slide

3. © Annie Patton Step 1: Given f(x) Step 2: Find f(x+h) Step 3: Find f(x+h)-f(x) Step 4: Find Step 5: Find 5 steps to Differentiate by first principles Next Slide

4. © Annie Patton Find from first principles the derivative of x 2 with respect to x. Step 1: f(x)=x 2 Step 2: f(x+h)=(x+h) 2 = x 2 +2xh+h 2 Step 3: f(x+h) - f(x)= x 2 +2xh+h 2 -x 2 Step 4: Step 5 Next Slide Leaving Certificate 2005 Higher Level Paper 1 no 7(a) Start clicking when you want to see the answer.

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

6. © Annie Patton Differentiate with respect to x from first principles. Next Slide Leaving Certificate 2007 Higher Level Paper 1 no 6(b)(i) Start clicking when you want to see the answer.

7. © Annie Patton Leaving Certificate 2007 Higher Level Paper 1 no 6(b)(i) Start clicking when you want to see the answer. Next Slide

8. © Annie Patton Next Slide Leaving Certificate 2001 Higher Level Paper 1 no 6(b)(i) Start clicking when you want to see the answer.

9. © Annie Patton Next Slide

10. © Annie Patton Next Slide

11. © Annie Patton Differentiate, from first principles, cos x with respect to x. Next Slide Leaving Certificate 2004 Higher Level Paper 1 no 6(b)(ii) Start clicking when you want to see the answer.

12. © Annie Patton Find from first principles the derivative of sinx with respect to x. Next Slide Leaving Certificate 1999 Higher Level Paper 1 no 6(b) Start clicking when you want to see the answer.

13. © Annie Patton 5 steps to Differentiate by first principles Next Slide Step 1: Given f(x) Step 2: Find f(x+h) Step 3: Find f(x+h)-f(x) Step 4: Find Step 5: Find

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

15. © Annie Patton Homework