y = (3x^4 + 1)^4 * (x^3 + 4)
To find the derivative, we're going to need to use a chain rule and a product rule.
y'= (3x^4 +1)^4 * d/dx (x^3 +4) + (x^3+4) * d/dx (3x^4 +1)^4
= (3x^4 +1)^4 * 3x^2 + (x^3+4) * 4(3x^4 +1)^3 * 12x
= 3x^2(3x^4 +1)^3 + 48x(x^3+4)(3x^4 +1)^3
From here, all you need to do is simplify the expression to get the textbook answer.
Oh, I see, didn't read your question thoroughly enough right away. Um, all you really should have to do is simplify the expression and then factor out a 3x^2(3x^4 + 1)^3 from the expression.