# Differentiate functions

I have two functions:

F1[t_, g_] := a1*t + a2*g

F2[t_, g_] := b1*t + b2*g

I want to evaluate (dt/dF1)F2(dt/dF1)F2(dt/dF1)_{F2}; i.e., differentiate ttt over F1F1 when F2F2 is held constant. Is there any straightforward way in Mathematica to do that with D.

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– Michael E2
Sep 15 ’15 at 18:19

thank you so much
– amin bk
Sep 17 ’15 at 17:34

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1

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I’m not used to your notation, but does this give you what you mean?

Block[{a1, a2, b1, b2},
SetAttributes[{a1, a2, b1, b2}, Constant];
Dt[t]/Dt[f1] /. First@Solve[
{Dt[f1] == Dt[F1[t, g]], 0 == Dt[F2[t, g]]},
{Dt[f1], Dt[t]}] // Simplify
]
(* b2/(-a2 b1 + a1 b2) *)

Yes, Thank you so much
– amin bk
Sep 15 ’15 at 19:15