From Rogawski ET section 3.10, exercise 35. Find the derivative using the method

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y= x^(3x) If y = x^(3x) and x > 0 then ln y = ln (x^(3x) ) Use properties of logarithmic functions to expand the right side of the above equation as follows. ln y = 3x ln x We now differentiate both sides with respect to x, using chain rule on the left side and the product rule on the right. y '(1 / y) =3 ln x + 3x(1 / x) = 3ln x + 3 , where y ' = dy/dx Multiply both sides by y y ' = 3(ln x + 1)y Substitute y by x x to obtain y ' = 3(ln x + 1)x^(3x)

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