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Question
Find `dy/dx`, if y = (log x)x.
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Solution
y = (log x)x
Taking log of both sides,
log y = x log (logx)
Differentiating w.r.t. x,
`1/y dy/dx = x d/dx [log (log x)] + log (log x) d/dx (x)`
= `x * 1/(log x) * 1/x + log (log x) (1)`
`therefore dy/dx = y [1/(log x) + log (logx)]`
`therefore dy/dx = (log x)^x [1/(log x) + log (log x)]`
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