easy differentiation... but three variables

so i have an equation x´ as a function of x and t
i make the substitution u=x/t
how do i get u´
thanks!

so i have an equation x´ as a function of x and t
i make the substitution u=x/t
how do i get u´
thanks!

post a picture of your question
I am teaching now but I will look at it tomorrow morning

Do the dashes denote derivatives or different functions? I'm struggling to follow this!

Thanks

so i have an equation x´ as a function of x and t
i make the substitution u=x/t
how do i get u´
thanks!

What is u' supposed to be? du/dt? du/dx? or something else??? Are x and t independent variables or is one a function of the other?

What is u' supposed to be? du/dt? du/dx? or something else??? Are x and t independent variables or is one a function of the other?

x´ is dx/dt
u´ is du/dt

In the question: x´ = (x/t) / (1+(x/t))
And I want to make the subst u=x/t

x´ is dx/dt
u´ is du/dt

In the question: x´ = (x/t) / (1+(x/t))
And I want to make the subst u=x/t

If u = x/t then x = tu so now you just use the product rule:

x' = (tu)'

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