Question: How to do composite differentiaition?

Please help me to differentiate function "u" wrt t in following manner:





DepVars := [F(xi), G(xi)]

[F(xi), G(xi)]


alias(F = F(xi), G = G(eta))

F, G


declare(F, G(xi))

F(xi)*`will now be displayed as`*F


G(xi)*`will now be displayed as`*G


u := a[0]+(F*a[1]+G*a[2]+kappa[1])/(mu[0]+mu[1]*(diff(F, xi))+mu[2]*(diff(G, eta)))+(F^2*a[3]+F*G*a[4]+G^2*a[5]+kappa[2])/(mu[0]+mu[1]*(diff(F, xi))+mu[2]*(diff(G, eta)))^2

a[0]+(a[1]*F+a[2]*G+kappa[1])/(mu[0]+mu[1]*(diff(F, xi))+mu[2]*(diff(G, eta)))+(a[3]*F^2+a[4]*F*G+a[5]*G^2+kappa[2])/(mu[0]+mu[1]*(diff(F, xi))+mu[2]*(diff(G, eta)))^2


xi := -t*c[1]*k[1]+x*k[1]; 1; eta := -t*c[2]*k[2]+x*k[2]





diff(u, t)

Error, invalid input: diff received -t*c[1]*k[1]+x*k[1], which is not valid for its 2nd argument




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