Mathematics
Selviaprianti1t
22

find derivative of y = x^(lnx), Show step-by-step solution

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(2) Answers
yasemina88

x^ln(x) =x^ln(x) * ln(x)*ln(x) =(ln^2(x))*x^ln(x) =2ln(x)*(ln(x)*x^ln(x))  =2x^ln(x)-1 * ln(x) 

petranajjar

y = x^(ln x )        / ln   ( we will logarithm both sides of the equation ) [latex]ln y = ln x^{lnx} \\ ln y = ln x * ln x \\ ln y = ln ^{2} x \\ \frac{1}{y}y`= 2 ln x * \frac{1}{x} \\ y`= \frac{2lnx}{x}*y \\ y`= \frac{2lnx*x ^{lnx} }{x} [/latex]

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