Find The Indicated Derivative: D/dx (x^(ln(x)/6))

Anonymous

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Find the indicated derivative: d/dx (x^(ln(x)/6))

 

Answer No.1

Anonymous

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Let y = x^(lnx)/6 6y = x^lnx ln(6y) =( lnx)^2 y'/y = 2lnx / x y' = x^(lnx)*lnx/3x ---------> ANSWER

Answer No.2

LondonDan5

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Let y = x^(lnx)/6 y = x^lnx/6 ln(y) =( lnx)^2/6 y'/y = 2lnx / 6x y' = (x^(ln(x)/6))*lnx/3x ---------> ANSWER

Answer No.3

Anonymous

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Given : d/dx(x(lnx)/6) assume y = x(lnx)/6 taking natural logarithm both side, we get ; lny = (lnx)lnx/6 or lny = (lnx)2 then d/dx for both side ; d(lny)/dx = d/dx(lnx)2 (1/y)dy/dx = 2lnx*(1/x) dy/dx = (2ylnx)x the value of y in dy/dx equation, we get ; dy/dx = (x(lnx)/6)*2*(lnx)/x = (2lnx)*(x(lnx)/6)/x

Answer No.4

Anonymous

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Y = x(lnx) /6 take logarithm on both sides ln y = ln [x(lnx) /6] ln y = [ln x ]/6 . ln x 1/y. dy/dx = (1/6) [ 1/x ln x + 1/x lnx] = (2/6) (ln x )/x dy/dx = y/x (1/3) ln x = (1/3x) ln x x(lnx) /6

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