Answer
$F'(x) = 24x^{11}(5x^3 + 2)(5x^3+1) $
Work Step by Step
Original Expression: $F(x) = (5x^6 + 2x^3)^4$
$u = 5x^6 + 2x^3$
$F(u) = x^4 $
Apply the chain rule: $f'(u) \times u'$
$F'(u) = 4(u)^3 30x^5 +6x^2$
$F'(x) = 4(5x^6 + 2x^3)^3 (30x^5 +6x^2)$
Simplify:
$4(x^3)^3(5x^3 + 2)6x^2(5x^3+1) $
$4x^9(5x^3 + 2)6x^2(5x^3+1) $
$24x^{11}(5x^3 + 2)(5x^3+1) $
