Partial differentiation

[lldk]

To find the partial u respect to t in this question and since v(t,x) = u(t-t₀, x-x₀), I differentiate u(t-t₀, x-x₀) respect to t and equal to u_x(t-t₀, x-x₀) But it seems I cannot find the answer if I do in this way. So may I ask how to do this question?

 

[Deleted member 4993]

To find the partial u respect to t in this question and since v(t,x) = u(t-t₀, x-x₀), I differentiate u(t-t₀, x-x₀) respect to t and equal to u_x(t-t₀, x-x₀) But it seems I cannot find the answer if I do in this way. So may I ask how to do this question?
View attachment 34026

To find the partial u respect to t in this question and since v(t,x) = u(t-t0, x-x0), I differentiate u(t-t0, x-x0) respect to t and equal to ux(t-t0, x-x0) But it seems I cannot find the answer

Please share your work in detail - so that we can catch your mistake/s (if there are any).

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING​

Please share your work/thoughts about this problem

 

[topsquark]

To find the partial u respect to t in this question and since v(t,x) = u(t-t₀, x-x₀), I differentiate u(t-t₀, x-x₀) respect to t and equal to u_x(t-t₀, x-x₀) But it seems I cannot find the answer if I do in this way. So may I ask how to do this question?
View attachment 34026

Hint: Think "chain rule."

-Dan