Question: Uses of chain rule to compute the derivaitve of higher order

Dear Users!

Hope everyone is fine here. Let me explain my problem first for this consider
diff(Y(xi), xi) = mu*(1-Y(xi)^2)
Then the derivative of a function U=u(Y(xi)) using chain rule (and expression menstiones as red) is given as,
diff(U, xi) = (diff(diff(Y, xi), Y))*U and (diff(diff(Y, xi), Y))*U = mu*(1-Y(xi)^2)*(diff(U, Y))
Similarly the second-order derivaitve of U=u(Y(xi)) using chain rule (and expression menstiones as red) is given as,
((ⅆ)^(2))/(ⅆ xi^(2))U=(ⅆ)/(ⅆ xi)(mu (1-Y^(2)(xi))*(ⅆ)/(ⅆ Y)U)=((ⅆ)/(ⅆ Y)*(ⅆ)/(ⅆ xi)Y)(mu (1-Y^(2)(xi))*(ⅆ)/(ⅆ Y)U)=(ⅆ)/(ⅆ Y)(mu^(2) (1-Y^(2)(xi))^(2)*(ⅆ)/(ⅆ Y)U)=-2 Y(xi) mu^(2) (1-Y^(2)(xi))*(ⅆ)/(ⅆ Y)U+ mu^(2) (1-Y^(2)(xi))^(2)*((ⅆ)^(2))/(ⅆ Y^(2))U;
In the similar way I want to compute the higher-order (like 5th order) derivaitve of U w.r.t. xi using the chain rule  (and expression menstiones as red) explained in above. Kindly help me soolve my problem

I am waiting for positive response.