Use logarithmic differentaition to find the derivative of the following?

Question

y= (x+1)^2((e^x)-1)^3/((2x^3)-5)^4

Answer 1

Oh man...

y= (x + 1)^2((e^x) - 1)^3/((2x^3) - 5)^4

lny = ln [(x+1)^2((e^x)-1)^3/((2x^3)-5)^4]
lny = ln [(x+1)^2((e^x)-1)^3] - ln[((2x^3)-5)^4]
lny = ln [(x+1)^2] + ln[((e^x)-1)^3] - ln[((2x^3)-5)^4]
lny = 2ln(x+1) + 3 ln[(e^x)-1] - 4 ln((2x^3)-5)

1/y * y' = 2/(x+1) + 3e^x / (e^x-1) - 24x^2 / (2x^3 - 5)
y' = y * 2/(x+1) + 3e^x/(e^x-1) - 24x^2/(2x^3 - 5)
y' = [(x+1)^2((e^x) - 1)^3/((2x^3) - 5)^4] * [2/(x + 1) + (3e^x)/((e^x) -1) - (24x^2)/(2x^3 - 5)]

Answer 2

Equation is incomplete