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Continuity And Differentiability

Question

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Differentiate $square root of 15 straight x squared minus straight x plus 1 end root straight w. straight r. straight t space straight x$

Solution

Let space space space space space space straight y equals square root of 15 straight x squared minus straight x plus 1 end root equals left parenthesis 15 straight x squared minus straight x plus 1 right parenthesis to the power of 1 half end exponent therefore space dy over dx equals 1 half left parenthesis 15 straight x squared minus straight x plus 1 right parenthesis to the power of negative 1 half end exponent straight d over dx left parenthesis 15 straight x squared minus straight x plus 1 right parenthesis space space space space space space space space space space space space space equals fraction numerator 1 over denominator 2 left parenthesis 15 straight x squared minus straight x plus 1 right parenthesis to the power of 1 half end exponent end fraction. left parenthesis 30 straight x minus 1 right parenthesis equals fraction numerator 30 straight x minus 1 over denominator 2 square root of left parenthesis 15 straight x squared minus straight x plus 1 right parenthesis end root end fraction

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