- #1

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## Main Question or Discussion Point

How would you differntiate the following type of formula:

d/dt [ e^(Integral from 0 to t [v(x+s,t-s) ds])f(x+t)]

Note: I dont want to change variables, I know I can make it nicer but I would like to know how to do it directly.

So far:

= e^(d/dt[integral from 0 to t(v(x+s,t-s)ds)]) * f(x+t) + e^(integral from 0 to t[v(x+s,t-s)ds]) * d/dt(f(x+t))

So I really just need help doing:

d/dt [ Integral from 0 to t (v(x+s,t-s)ds)]

= v(x+s,t-s) right? I'm not sure about this.

d/dt [ e^(Integral from 0 to t [v(x+s,t-s) ds])f(x+t)]

Note: I dont want to change variables, I know I can make it nicer but I would like to know how to do it directly.

So far:

= e^(d/dt[integral from 0 to t(v(x+s,t-s)ds)]) * f(x+t) + e^(integral from 0 to t[v(x+s,t-s)ds]) * d/dt(f(x+t))

So I really just need help doing:

d/dt [ Integral from 0 to t (v(x+s,t-s)ds)]

= v(x+s,t-s) right? I'm not sure about this.