回答:
#(d y)/(d x)= 4/3 * x ^( - 2/3)+ 8/3 * x ^(1/3) "(一次導関数)"#
#(d ^ 2 y)/(d t ^ 2)= 8/9 * x ^( - 2/3)( - x ^ -1 + 1) "(二階微分)"#
説明:
#y = 4x ^(1/3)+ 2x ^(4/3)#
#(d y)/(d x)= 1/3 * 4 * x ^((1 / 3-1))+ 4/3 * 2x ^((4 / 3-1))#
#(d y)/(d x)= 4/3 * x ^( - 2/3)+ 8/3 * x ^(1/3) "(一次導関数)"#
#(d ^ 2 y)/(dt ^ 2)= - 2/3 * 4/3 * x ^(( - 2 / 3-1))+ 8/3 * 1/3 * x ^((1 / 3-1))#
#(d ^ 2 y)/(d t ^ 2)= - 8/9 * x ^(( - - 5/3))+ 8/9 * x ^(( - 2/3)#
#(d ^ 2 y)/(d t ^ 2)= 8/9 * x ^( - 2/3)( - x ^ -1 + 1) "(二階微分)"#