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Question

If 5 f left parenthesis x right parenthesis plus 3 f left parenthesis fraction numerator 1 over denominator x end fraction right parenthesis equals x plus 2 andy equals x f (x)then fraction numerator d y over denominator d x end fraction at x=1 is

  1. 14    
  2. 7 divided by 8    
  3. 1    
  4. None    

The correct answer is: 7 divided by 8


    5 f left parenthesis x right parenthesis plus 3 f left parenthesis 1 divided by x right parenthesis equals x plus 2 horizontal ellipsis horizontal ellipsis horizontal ellipsis horizontal ellipsis left parenthesis 1 right parenthesis put fraction numerator 1 over denominator x end fraction for x
    3 f left parenthesis x right parenthesis plus 5 f left parenthesis 1 divided by x right parenthesis equals fraction numerator 1 over denominator x end fraction plus 2 horizontal ellipsis horizontal ellipsis horizontal ellipsis.. left parenthesis 2 right parenthesis
    Solving 1 & 216 f left parenthesis x right parenthesis equals 5 x minus fraction numerator 3 over denominator x end fraction plus 4
    y equals fraction numerator 1 over denominator 16 end fraction left square bracket 5 x to the power of 2 end exponent plus 4 x minus 3 right square bracket
    fraction numerator d y over denominator d x end fraction equals fraction numerator 10 x plus 4 over denominator 16 end fraction at x equals 1 equals fraction numerator d y over denominator d x end fraction equals fraction numerator 7 over denominator 8 end fraction

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