Use logarithmic differentiation to find the derivative of the function

Question

Find y':

y= √ ((x-1)/(x^(8)+2))

Answer 1

y = √(x-1) / (x⁸ + 2)

lny = ln [√(x-1) / (x⁸ + 2) ]

lny = (1/2)ln(x-1) - ln(x⁸ +2)

y' / y = 1 / (2(x-1) - 8x⁷ / (x⁸ + 2)

y' = y[ 1/(2x-2) - 8x⁷/ (x⁸ +2) ]

y' = √(x-1) / (x⁸ + 2) [ 1/(2x-2) - 8x⁷ / (x⁸+2) ]