Question

Differentiate (a^x)^x w.r.t.x.

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Solution

Let space straight y equals left parenthesis straight x to the power of straight x right parenthesis to the power of straight x equals straight x to the power of straight x squared end exponent therefore space log space straight y equals log space straight x to the power of straight x squared end exponent space rightwards double arrow log space straight y equals straight x squared. log space straight x Diff. space straight w. straight r. straight t. space straight x. space 1 over straight y dy over dx equals straight x squared 1 over straight x plus left parenthesis log space straight x right parenthesis.2 straight x therefore space dy over dx equals straight y left square bracket straight x plus 2 straight x space log space straight x right square bracket equals straight x squared left square bracket straight x plus 2 space straight x space log space straight x right square bracket.

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