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Continuity And Differentiability

Question

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Differentiate the following w.r.t.x:
$log space 10 left parenthesis straight x squared plus 3 straight x minus 1 right parenthesis$

Solution

Let space straight y equals log space 10 left parenthesis straight x squared plus 3 straight x minus 1 right parenthesis equals fraction numerator log left parenthesis straight x squared plus 3 straight x minus 1 right parenthesis over denominator log space 10 end fraction therefore space space space space space space space straight y equals fraction numerator 1 over denominator log space 10 end fraction left square bracket log space left parenthesis straight x squared plus 3 straight x minus 1 right parenthesis right square bracket therefore space dy over dx equals fraction numerator 1 over denominator log space 10 end fraction open square brackets fraction numerator 1 over denominator straight x squared plus 3 straight x minus 1 end fraction. straight d over dx left parenthesis straight x squared plus 3 straight x minus 1 right parenthesis close square brackets space space space space space space space space space space space space space equals fraction numerator 1 over denominator log space 10 end fraction open square brackets fraction numerator 1 over denominator straight x squared plus 3 straight x minus 1 end fraction cross times left parenthesis 2 straight x plus 3 right parenthesis close square brackets equals fraction numerator 2 straight x plus 3 over denominator left parenthesis straight x squared plus 3 straight x minus 1 right parenthesis log space 10 end fraction

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