Find the derivative of the following : from Mathematics Limits
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    Limits and Derivatives

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    41. Find the derivative of the following :


    space space space space space space space space fraction numerator 2 over denominator straight x plus 1 end fraction minus fraction numerator straight x squared over denominator 3 straight x minus 1 end fraction

    Let               space space space space space space space space space space space space space straight y space equals space fraction numerator 2 over denominator straight x plus 1 end fraction minus fraction numerator straight x squared over denominator 3 straight x minus 1 end fraction

    Differentiating both sides w.r.t. x, we get


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       space space space space space space space space space space space space space space equals space 2 space straight d over dx left parenthesis straight x plus 1 right parenthesis to the power of negative 1 end exponent minus fraction numerator left parenthesis 3 straight x minus 1 right parenthesis begin display style straight d over dx end style straight x squared minus straight x squared space begin display style straight d over dx end style left parenthesis 3 straight x minus 1 right parenthesis over denominator left parenthesis 3 straight x minus 1 right parenthesis squared end fraction

         space space space space space space space space space space space space space space space space space space equals space fraction numerator negative 2 over denominator left parenthesis straight x plus 1 right parenthesis squared end fraction minus fraction numerator 6 straight x squared minus 2 straight x minus 3 straight x squared over denominator left parenthesis 3 straight x minus 1 right parenthesis end fraction equals fraction numerator negative 2 over denominator left parenthesis straight x plus 1 right parenthesis squared end fraction minus fraction numerator 3 straight x squared minus 2 straight x over denominator left parenthesis 3 straight x minus 1 right parenthesis end fraction

      

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    42. Find the derivative of the following :



    space space space space space space space fraction numerator 1 plus begin display style 1 over straight x end style over denominator 1 minus begin display style 1 over straight x end style end fraction
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    43. Find the derivatives of the following :

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    44. Find the derivatives of the following :

    (ax+b)n (cx+ d)n 
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    45. Derivative of xn.
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    46.

    Derivative of (ax + b)n, n being a rational number.

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    47. Derivative of sin x :
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    48. Find the derivatives of the following functions :

    x100 
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    49. Find the derivatives of the following functions :

    6x100 - x55 + x
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    50. Find the derivatives of the following functions :

    space space space fraction numerator 1 over denominator square root of straight x end fraction
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