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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