$f'(x) = (\frac{3}{2} \times \frac{1}{{2\sqrt x }}){({x^2} + 6x)^2} + 2(2x + 6)({x^2} + 6x)(\frac{3}{2}\sqrt x )$ $f'(4) = (\frac{3}{2} \times \frac{1}{{2 \times 2}}){(16 + 24)^2} + 2(8 + 6)(16 + 24)(\frac{3}{2} \times 2)$$ = \frac{3}{8} \times 1600 + 2 \times 14 \times 40 \times 3$$ = 600 + 3360 = 3960$