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I don't believe that the answer is ln(x)x^(ln(x)-2), since the power rule doesn't apply when you have the variable in the exponent. Do the following instead:y x^ln(x)
Taking the natural log of both sides:ln(y)ln(x) * ln(x)ln(y) ln(x)^2
Take the derivative of both sides, using the chain rule:1/y * y' 2 ln(x) / xy' 2 ln(x)/ x * y
Finally, substitute in the first equation, y x^ln(x):y' 2 ln(x) / x * x^ln(x)y'2 ln(x) * x ^ (ln(x) - 1)
Sorry if everything is formatted really badly, this is my first post on answers.com.
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What is the derivative of 2 to the power of x?
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What is 2 divided by x as a power of x?
x^(ln(2)/ln(x)-1)
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Differentiate log x?
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