Upcoming SlideShare
Loading in …5
×

# 11 x1 t09 08 implicit differentiation (2013)

648 views

Published on

Published in: Education, Technology
• Full Name
Comment goes here.

Are you sure you want to Yes No
Your message goes here
• Be the first to comment

• Be the first to like this

### 11 x1 t09 08 implicit differentiation (2013)

1. 1. Differentiability
2. 2. DifferentiabilityA function is differentiable at a point if the curve is smooth continuous   i.e. lim limx a x af x f x   
3. 3. DifferentiabilityA function is differentiable at a point if the curve is smooth continuous   i.e. lim limx a x af x f x   yx111y x 
4. 4. DifferentiabilityA function is differentiable at a point if the curve is smooth continuous   i.e. lim limx a x af x f x   yx111y x not differentiable at x = 1
5. 5. DifferentiabilityA function is differentiable at a point if the curve is smooth continuous   i.e. lim limx a x af x f x   yx111y x  1lim 1xf x  not differentiable at x = 1
6. 6. DifferentiabilityA function is differentiable at a point if the curve is smooth continuous   i.e. lim limx a x af x f x   yx111y x  1lim 1xf x    1lim 1xf x not differentiable at x = 1
7. 7. DifferentiabilityA function is differentiable at a point if the curve is smooth continuous   i.e. lim limx a x af x f x   yx111y x  1lim 1xf x    1lim 1xf x not differentiable at x = 1yx2y x
8. 8. DifferentiabilityA function is differentiable at a point if the curve is smooth continuous   i.e. lim limx a x af x f x   yx111y x  1lim 1xf x    1lim 1xf x not differentiable at x = 1yx2y x1
9. 9. DifferentiabilityA function is differentiable at a point if the curve is smooth continuous   i.e. lim limx a x af x f x   yx111y x  1lim 1xf x    1lim 1xf x not differentiable at x = 1yx2y x1differentiable at x = 1
10. 10. Implicit Differentiation
11. 11. Implicit Differentiationdf df dydx dy dx 
12. 12. Implicit Differentiationdf df dydx dy dx 2e.g. (i) x y
13. 13. Implicit Differentiationdf df dydx dy dx 2e.g. (i) x y   2d dx ydx dx
14. 14. Implicit Differentiationdf df dydx dy dx 2e.g. (i) x y   2d dx ydx dx   2 2d d dyy ydx dy dx 
15. 15. Implicit Differentiationdf df dydx dy dx 2e.g. (i) x y1 2dyydx   2d dx ydx dx   2 2d d dyy ydx dy dx 
16. 16. Implicit Differentiationdf df dydx dy dx 2e.g. (i) x y1 2dyydx   2d dx ydx dx12dydx y   2 2d d dyy ydx dy dx 
17. 17. Implicit Differentiationdf df dydx dy dx 2e.g. (i) x y1 2dyydx   2d dx ydx dx12dydx y   2 2d d dyy ydx dy dx  2 3(ii)dx ydx
18. 18. Implicit Differentiationdf df dydx dy dx 2e.g. (i) x y1 2dyydx   2d dx ydx dx12dydx y   2 2d d dyy ydx dy dx  2 3(ii)dx ydx    2 2 33 2dyx y y xdx    
19. 19. Implicit Differentiationdf df dydx dy dx 2e.g. (i) x y1 2dyydx   2d dx ydx dx12dydx y   2 2d d dyy ydx dy dx  2 3(ii)dx ydx    2 2 33 2dyx y y xdx    2 2 33 2dyx y xydx 
20. 20.    2 2Find the equation of the tangent to 9 at the point 1,2 2iii x y 
21. 21.    2 2Find the equation of the tangent to 9 at the point 1,2 2iii x y 2 29x y 
22. 22.    2 2Find the equation of the tangent to 9 at the point 1,2 2iii x y 2 29x y 2 2 0dyx ydx 
23. 23.    2 2Find the equation of the tangent to 9 at the point 1,2 2iii x y 2 29x y 2 2 0dyx ydx 2 2dyy xdx 
24. 24.    2 2Find the equation of the tangent to 9 at the point 1,2 2iii x y 2 29x y 2 2 0dyx ydx 2 2dyy xdx dy xdx y 
25. 25.    2 2Find the equation of the tangent to 9 at the point 1,2 2iii x y 2 29x y 2 2 0dyx ydx 2 2dyy xdx dy xdx y   1at 1,2 2 ,2 2dydx 
26. 26.    2 2Find the equation of the tangent to 9 at the point 1,2 2iii x y 2 29x y 2 2 0dyx ydx 2 2dyy xdx dy xdx y   1at 1,2 2 ,2 2dydx 1required slope2 2  
27. 27.    2 2Find the equation of the tangent to 9 at the point 1,2 2iii x y 2 29x y 2 2 0dyx ydx 2 2dyy xdx dy xdx y   1at 1,2 2 ,2 2dydx 1required slope2 2   12 2 12 2y x   
28. 28.    2 2Find the equation of the tangent to 9 at the point 1,2 2iii x y 2 29x y 2 2 0dyx ydx 2 2dyy xdx dy xdx y   1at 1,2 2 ,2 2dydx 1required slope2 2   12 2 12 2y x   2 2 8 1y x   
29. 29.    2 2Find the equation of the tangent to 9 at the point 1,2 2iii x y 2 29x y 2 2 0dyx ydx 2 2dyy xdx dy xdx y   1at 1,2 2 ,2 2dydx 1required slope2 2   12 2 12 2y x   2 2 8 1y x   2 2 9 0x y  
30. 30.    2 2Find the equation of the tangent to 9 at the point 1,2 2iii x y 2 29x y 2 2 0dyx ydx 2 2dyy xdx dy xdx y   1at 1,2 2 ,2 2dydx 1required slope2 2   12 2 12 2y x   2 2 8 1y x   2 2 9 0x y  Exercise 7K; 1acegi, 2bdfh, 3a,4a, 7, 8