IGCSE math Differentiation-introduction_2.pptx

IGCSE math Differentiation-introduction_2.pptx

1. Chapter 22 Differentiation

2. Power Rule (also called gradient function)  

3. Starter         ? ? ? ?   ? 1 2 3 4 5

4. Objectives: Find dy /dx Find the gradient at a point

5. Objectives Differentiating Multiple Terms

6. Differentiating Multiple Terms Differentiate   First thing to note: If then i.e. differentiate each term individually in a sum/subtraction .     ? ? ? Therefore applying the usual rule: Alternatively, if you compare to , it’s clear that the gradient is fixed and .   Therefore applying the usual rule: Alternatively, if you sketch , the line is horizontal, so the gradient is 0.  

7. Activity   1 2 3 4 5         ? ? ? ? ? (where is a constant)   (where is a constant)   6   ?

8. Activity   1 2 3 4 5 2x-6   4x     +7   ? ? ? ? ?

9. Harder Example Let y Find Find the gradient of at the point Find the coordinates of the point on the graph of where the gradient is 8.     Remember that the ‘gradient function’ allows you to find the gradient for a particular value of .   =8 Point is   This example is important! Previously you used a value of to get the gradient . This time we’re doing the opposite : using a known gradient to get the value of . We therefore substitute for 8.   a b Once you have your , you need to work out . Ensure you use the correct equation!   ? ? c

10. Test Your Understanding Let Find Find the gradient of at the point Find the coordinates of the point on the graph of where the gradient is 5. c) Find the coordinates of the point on the graph of where the gradient is 0.   G radient at(1,-1)   , 2x = 4+5 = 9 Point is   b c d 2x = 4 X = 2 Y = (2 )2- 4(2) +2 = -2 Point is (2,-2)   ? ? ?

11. Activity: Choose any one and solve b

12. Plenary For each of the following, find the gradient function , and hence find the gradient of the tangent to the curve when The tangent to the curve has gradient 6. Determine the possible values of .   For the curve , determine: The gradient of the tangent to the curve at the point The point on the curve where the gradient is 5. Find the points on the curve where the gradient is 11.   1 2 3 4 a b c d e f g ? ? ? ? ? ? ? ? ? ? ?

13. H.W. Exercise 22A Q1 or Q4