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Thanks much. However, I have found a better way as follows: a=matrix([[x3+t,2,(x3)],[t^2,5,x3],[t,x3,x3^2]])

ac=copy(a)

b=derivative(ac,t);b

c=derivative(ac,x3);c

var('dx3')

d=b+dx3*c;d

[ dx3 + 1, 0 , dx3]

[ 2*t, 0, dx3]

[ 1, dx3, 2dx3x3]

Thanks much. However, I have found a better way as ~~follows: a=matrix([[x3+t,2,(x3)],[t^2,5,x3],[t,x3,x3^2]])~~follows:

ac=copy(a)

b=derivative(ac,t);b

c=derivative(ac,x3);c

var('dx3')

d=b+dx3*c;d

sage: t, x3, dx3 = var('t x3 dx3') sage: a = matrix([[x3+t,2,x3],[t^2,5,x3],[t,x3,x3^2]]) sage: b = derivative(a,t); b [ 1 0 0] [2*t 0 0] [ 1 0 0] sage: c = derivative(a,x3); c [ 1 0 1] [ 0 0 1] [ 0 1 2*x3] sage: d = b+dx3*c; d [ dx3 + 1, 0 , dx3] [ 2*t, 1 0, 0 dx3] dx3] [ 2*t 0 dx3] [ 1, 1 dx3, 2dx3x3]dx3 2*dx3*x3]