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Basic Differentiation

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different types of problems to excel in differentiation
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  DIFFERENTIATION PAPER 1 1.Given the curve 38)(  2 +−−=  x x x  f   . Find the maximum point of the curve.[3 marks ]  Answer :  ………………………..….2.Given that r cm is the radius of a sphere. Cacuate the approximate chan!e in its area henthe radius increases from 8 cm to 8.##2 cm. [$ marks ]  Answer :  ………………………..….3.Find      − 3%1  xdxd  .[2 marks ]  Answer :  ………………………..….1  $.Given that 3% 2 +−=  x x y . Find (a)the coordinates of the point hen the curve intersects the  y &axis. (')the !radient of the tan!ent at point (1 &1).[$ marks ]  Answer   (a)……………………..…(')……………………….%.Given that 2 $%  x y  −= . Find the approximate chan!e in  y   hen  x  decreases from 3 to2.*8.[$ marks ]  Answer :  ………………………..….+.,he point  P   ies on the curve  y  - (  x   −  %) 2 . t is !iven that the !radient of the norma at  P  is 1$ − . Find the coordinates of  P  .[3 mar/s]2   Answer :  ………………………..….0. Given that % )13()(  +=  x x  f   . Find the vaue of  f’  (&1). [3 marks ]  Answer :  ………………………..….8.t is !iven that 0 32 u y  =  here %3  −=  xu . Find dydx in terms of  x .[3 mar/s]  Answer :  ………………………..….*.,he area of a sphere increases at a rate of $.2 π  cm 2 s &1   hen it is heated. Find(a)the rate of chan!e of the radius hen the radius is 3 cm(')the rate of chan!e of the voume at that instant. [$ marks ]  Answer   (a)……………………..…3  (')……………………….1#. Given that 2$2 −+=  x x y  and 2 )2(  −=  xk dxdy . Find the vaue of k  .[3 marks ]  Answer :  ………………………..….11.Given that 2 3 $  y x x = + − (a)find the vaue of dydx hen  x  - 1(')express the approximate chan!e in  y  in terms of  p  hen  x  chan!es from 1 to1   p  here  p  is a sma vaue.[$ mar/s]  Answer   (a)……………………..…(')……………………….$
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