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- rule = Times[f[x, t],
- Derivative[1, 0][y_][x, t]] :> (P[y] - D[y[x, t], t]);
- A = (D[w[x, t], t]+f[x, t]*D[w[x, t], x])*(1 + (D[q[x, t], t] +f[x, t]*D[q[x, t], x]));
- A /. rule
- (* (1 + P[q]) P[w] *)
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