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

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  • 1. Differentiability
  • 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. 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. 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. 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. 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. 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. 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. 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. Implicit Differentiation
  • 11. Implicit Differentiationdf df dydx dy dx 
  • 12. Implicit Differentiationdf df dydx dy dx 2e.g. (i) x y
  • 13. Implicit Differentiationdf df dydx dy dx 2e.g. (i) x y   2d dx ydx dx
  • 14. Implicit Differentiationdf df dydx dy dx 2e.g. (i) x y   2d dx ydx dx   2 2d d dyy ydx dy dx 
  • 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. 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. 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. 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. 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.    2 2Find the equation of the tangent to 9 at the point 1,2 2iii x y 
  • 21.    2 2Find the equation of the tangent to 9 at the point 1,2 2iii x y 2 29x y 
  • 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.    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.    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.    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.    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.    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.    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.    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.    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

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