f(x)=(x^3+1)(2x^2+8x-5)
f'(x)=(x^3+1)'(2x^2+8x-5)+(x^3+1)(2x^2+8x-5)'
=3x^2(2x^2+8x-5)+(x^3+1)(4x+8)
=6x^4+24x^3-15x^2+4x^4+8x^3+4x+8
=10x^4+32x^3-15x^2+4x+8