Use logarithmic differentiation to find the derivative. y= squrt ((x-1)/(x^4-1))

Question

y= sqrt (x-1)/x⁴-1)

Answer 1

y = (x-1)/(x⁴-1)

ln(y) = ln(x-1) - ln(x⁴-1)

y'/y = 1/(x-1) - 4x³/(x⁴-1)

dy/dx = y[1/(x-1) - 4x³/(x⁴-1)] = ((x-1)/(x⁴-1))[1/(x-1) - 4x³/(x⁴-1)]

= 1/(x⁴-1) - 4(x-1)/(x⁴-1)²