Question

Differentiate ^{x(1 + log x)}w.r.t.x.

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Solution

Let space space space space space space straight y equals straight e to the power of straight x left parenthesis 1 plus log space straight x right parenthesis end exponent therefore space dy over dx equals straight e to the power of straight x left parenthesis 1 plus log space straight x right parenthesis end exponent. straight d over dx left square bracket straight x left parenthesis 1 plus log space straight x right parenthesis right square bracket space space space space space space space space space space space space space equals straight e to the power of straight x left parenthesis 1 plus log space straight x right parenthesis end exponent. open square brackets straight x straight d over dx left parenthesis 1 plus log space straight x right parenthesis plus left parenthesis 1 plus log space straight x right parenthesis. straight d over dx left parenthesis straight x right parenthesis close square brackets space space space space space space space space space space space space space equals straight e to the power of straight x left parenthesis 1 plus log space straight x right parenthesis end exponent. open square brackets straight x.1 over straight x plus left parenthesis 1 plus log space straight x right parenthesis.1 close square brackets space space space space space space space space space space space space space equals straight e to the power of straight x left parenthesis 1 plus log space straight x right parenthesis end exponent. left square bracket 1 plus 1 plus log space straight x right square bracket equals straight e to the power of straight x left parenthesis 1 plus log space straight x right parenthesis end exponent left parenthesis 2 plus log space straight x right parenthesis

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Continuity And Differentiability

Differentiate ^{x(1 + log x)}w.r.t.x.

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Continuity And Differentiability

Differentiate x(1 + log x)w.r.t.x.

Some More Questions From Continuity and Differentiability Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Differentiate ^{x(1 + log x)}w.r.t.x.