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Question: Differentiation of compound expressions

Question:Differentiation of compound expressions

Grigoriy Yashin 20 Maple 2020
differentiation implicit-differentation diff
May 14 2020
2

I try to take a partial derivative of compound expressions. Usage of diff, Diff, substitution variables instead of time-variant variables (subs) couldn't help me.

restart; PDEtools[declare](`θ__l`(t), `β__l`(t), `θ__si`(t), `β__si`(t), psi(t), x(t), z(t)); PDEtools[declare](prime = t); V__1lx := diff(x(t), t)-(1/2)*l__b*sin(psi(t))*(diff(psi(t), t))-l__1c*sin(`θ__l`(t)-psi(t))*(diff(`θ__l`(t), t)-(diff(psi(t), t))); V__1lz := diff(z(t), t)-(1/2)*l__b*cos(psi(t))*(diff(psi(t), t))-l__1c*cos(`θ__l`(t)-psi(t))*(diff(`θ__l`(t), t)-(diff(psi(t), t))); V__1l := simplify(V__1lx^2+V__1lz^2, size); diff(V__1l, psi); Diff(V__1l, psi)

Diff((diff(x(t), t)-(1/2)*l__b*sin(psi(t))*(diff(psi(t), t))+l__1c*sin(-theta__l(t)+psi(t))*(diff(theta__l(t), t)-(diff(psi(t), t))))^2+(diff(z(t), t)-(1/2)*l__b*cos(psi(t))*(diff(psi(t), t))-l__1c*cos(-theta__l(t)+psi(t))*(diff(theta__l(t), t)-(diff(psi(t), t))))^2, psi)

 (1)

``


Download DiffExpr.mw

Should I use implicitdiff? If yes, how does it work?

Also, I don't understand, why the derivative of theta_l is displayed so strange, as if the derivative is taken from the index l?

P.S. This question is a continuation of my last topic: https://www.mapleprimes.com/questions/229551-Operations-On-Several-Defined-Functions
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