Find f'(x) where f(x)= from Mathematics Continuity and Differen
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    Continuity and Differentiability

    Multiple Choice QuestionsShort Answer Type

    161.  Differentiate the following w.r.t.x: cube root of 2 straight x to the power of 4 plus straight x squared minus straight x end root
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    162. Differentiate the following w.r.t.x:fraction numerator 3 over denominator left parenthesis 2 straight x squared plus 5 right parenthesis squared end fraction
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    163. Differentiate the following w.r.t.x: square root of fraction numerator straight x squared minus 2 ax over denominator straight a squared minus 2 ab end fraction end root
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    164. Differentiate the following w.r.t.x:square root of fraction numerator 1 plus straight x over denominator 1 minus straight x end fraction end root
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    165. Differentiate the following w.r.t.x:square root of fraction numerator 1 minus straight x squared over denominator 1 plus straight x squared end fraction end root
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    166.

    Find f'(x) where f(x)=square root of fraction numerator 1 minus straight x over denominator 2 plus straight x end fraction end root

    straight f left parenthesis straight x right parenthesis equals square root of fraction numerator 1 minus straight x over denominator 2 plus straight x end fraction end root equals open parentheses fraction numerator 1 minus straight x over denominator 2 plus straight x end fraction close parentheses to the power of 1 half end exponent Differentiating space straight w. straight r. straight t space straight x comma space we space get straight f apostrophe left parenthesis straight x right parenthesis equals 1 half open parentheses fraction numerator 1 minus straight x over denominator 2 plus straight x end fraction close parentheses to the power of negative 1 half end exponent straight d over dx open parentheses fraction numerator 1 minus straight x over denominator 2 plus straight x end fraction close parentheses space space space space space space space space equals 1 half open parentheses fraction numerator 2 plus straight x over denominator 1 minus straight x end fraction close parentheses to the power of 1 half end exponent open square brackets fraction numerator left parenthesis 2 plus straight x right parenthesis begin display style straight d over dx end style left parenthesis 1 minus straight x right parenthesis minus left parenthesis 1 minus straight x right parenthesis begin display style straight d over dx end style left parenthesis 2 plus straight x right parenthesis over denominator left parenthesis 2 plus straight x right parenthesis squared end fraction close square brackets space space space space space space space space equals 1 half fraction numerator left parenthesis 2 plus straight x right parenthesis to the power of bevelled 1 half end exponent over denominator left parenthesis 1 minus straight x right parenthesis to the power of bevelled 1 half end exponent end fraction open square brackets fraction numerator left parenthesis 2 plus straight x right parenthesis left parenthesis negative 1 right parenthesis minus left parenthesis 1 minus straight x right parenthesis left parenthesis 1 right parenthesis over denominator left parenthesis 2 plus straight x right parenthesis squared end fraction close square brackets equals 1 half fraction numerator left parenthesis 2 plus straight x right parenthesis to the power of bevelled 1 half end exponent over denominator left parenthesis 1 minus straight x right parenthesis to the power of bevelled 1 half end exponent end fraction open square brackets fraction numerator negative 2 minus straight x minus 1 plus straight x over denominator left parenthesis 2 plus straight x right parenthesis squared end fraction close square brackets space space space space space space space space equals 1 half fraction numerator left parenthesis 2 plus straight x right parenthesis to the power of begin display style 1 half end style end exponent over denominator left parenthesis 1 minus straight x right parenthesis to the power of begin display style 1 half end style end exponent end fraction cross times fraction numerator negative 3 over denominator left parenthesis 2 plus straight x right parenthesis squared end fraction equals negative fraction numerator 3 over denominator 2 left parenthesis 1 minus straight x right parenthesis to the power of begin display style 1 half end style end exponent left parenthesis 2 plus straight x right parenthesis to the power of begin display style 3 over 2 end style end exponent end fraction
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    167. Differentiate square root of 3 straight x squared plus 2 straight x end root w.r.t x.
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    168. Differentiatefraction numerator 1 over denominator straight x plus square root of 1 plus straight x squared end root end fraction w.r.t x.
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    169. If space straight y equals open parentheses straight x plus square root of straight x squared plus straight a squared end root close parentheses to the power of straight n comma space prove space that space dy over dn equals fraction numerator ny over denominator square root of straight x squared plus straight a squared end root end fraction.
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    170. Differentiate x(1 + log x)w.r.t.x.
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