ln y = ln (x^3 + 2)^2 (x^5 + 4)^4
ln y = 2 ln (x^3 + 2) + 4 ln(x^5 + 4)
y' 1/y = 2 * 3x^2 * 1 / ( x^3 + 2) + 4 * 5x^4 * 1 / (x^5 + 4)
= 6x^2 / (x^3 + 2) + 20x^4 / ( x^5 + 4)
y' = y * (6x^2 / (x^3 + 2) + 20x^4 / ( x^5 + 4))
= 6x^2 (x^3 + 2)^2 (x^5 + 4)^4 + 20x^4 (x^3 + 2)^2 (x^5 + 4)^4
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(x^3 + 2) (x^5 + 4)
= 6x^2 ( x^3 + 2)(x^5 + 4)^3 + 20x^4(x^3 + 2)(x^5 + 4)^3
= 2x^2(3 + 10x^2)(x^3 + 2)(x^4 + 5)^3 Answer
