h(x)=(x2+10)2(x-10).
Let u=(x2+10)2, then du/dx=4x(x2+10), d2u/dx2=4(x2+10)+8x2=4(3x2+10); let v=x-10, then dv/dx=1, d2v/dx2=0.
h=uv, dh/dx=udv/dx+vdu/dx=(x2+10)2+4x(x-10)(x2+10).
Expanding: dh/dx=x4+20x2+100+4x(x3+10x-10x2-100),
dh/dx=5x4-40x3+60x2-400x+100, the first derivative, d2h/dx2=20x3-120x2+120x-400, the second derivative.
d2h/dx2=0+2(du/dx)(dv/dx)+vd2u/dx2=8x(x2+10)+4(x-10)(3x2+10).
d2h/dx2=8x3+80x+4(3x3+10x-30x2-100),
d2h/dx2=20x3-120x2+120x-400, which confirms the above calculation of the second derivative.