Differentiate y = x5√x. SOLUTION Since both the base and the exponent are variable, we use logarithmic differentiation: ln y = ln x5√x = 5 x ln(x) y' y = 5 x · + (ln(x)) · y' = y + 5 ln(x) = x5√x . Another method is to write x5√x = eln(x) 5√x : d dx x5√x = d dx = d dx 5 x ln(x) = x5√x .