I think what you will want to do is to write x as x[t] andjasj[t], so the equation would be:

x''[t]Š1/(M+m Sin[j[t]]^2) *(m Sin[j[t]] (g Cos[j[t]]+ l j'[t]^2)-D x'[t]+F u)

and to take the partial derivative with respect to x, you would write:D[x''[t]Š1/(M+m Sin[j[t]]^2) *(m Sin[j[t]] (g Cos[j[t]]+ l j'[t]^2)-D x'[t]+F u),x]which givesx(3)[t]=(D x''[t])/(M+m Sin[j[t]]2)