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09 Techniques of Differentiation

# 09 Techniques of Differentiation - 9 1 Find dy dx...

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9. TECHNIQUES OF DIFFERENTIATION 1. Find   dx dy   in each of the following cases. (a) [3 marks] y  =  e cos  x      __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ (b)[4 marks] y 2  ( xy  – 6) =  x 3     __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ (c) [4 marks] dt e y t x x ) sin( - = __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ VET  Calculus 50 9. Techniques of Differentiation

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2. Consider the function   f  ( x ) =  axe bx   where  a  and  b  are constants. (a) [3 marks] Find  f  ‘ ( x ) and  f  ‘’ ( x  ). __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ (b)[6 marks] Determine values for  a  and  b  so that  f  has a maximum of 1 at  ½ .  Justify your answer  using your answer to part (a). __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ VET  Calculus 51 9. Techniques of Differentiation
__________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ VET  Calculus 52 9. Techniques of Differentiation

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3. Find   dx dy   in each of the following cases. (a) [4 marks] y  =  e x   cos ( x 2  + 1) __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ (b)[4 marks] y  =   4 sin 3 2 3 + + x x x __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ (c) [3 marks] = x dt t y 7 1 1 __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ VET  Calculus 53 9. Techniques of Differentiation
__________________________________________________________________________________ __________________________________________________________________________________ VET  Calculus 54 9. Techniques of Differentiation

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4.
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09 Techniques of Differentiation - 9 1 Find dy dx...

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