y = (x^4+4)^2 (x^3+4)^4
ln y = 2ln(x^4+4) + 4ln(x^3+4)
1/y y' = 8x^3/(x^4+4) + 12x^2/(x^3+4)
y' =
[8x^3/(x^4+4) + 12x^2/(x^3+4)]*[(x^4+4)^2 (x^3+4)^4]
Now you can massage that as you will. Eventually you can arrive at
y' = 4x^2 (x^3+4)^3 (x^4+4) (5x^2+8x+12)
Use logarithmic differentiation to find the derivative of the function.
y = (x^4 + 2)^2(x^3 + 4)^4
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