(* Examples of Thread *)var = {x, y, z} ; val = {a, b, c} ; rule = Thread[varval] ; Cos[x + y + z]/.rule

Out[270]=

Cos[a + b + c]

In[271]:=

df = {p '[t], q '[t]} ;

fun = {-D[V, t], p/m} ;

Thread[dffun]

Out[273]=

{p^′[t] 0, q^′[t] p/m}

In[274]:=

(* Examples of Map (or /@) *)# '[t] & /@ var

Out[274]=

{x^′[t], y^′[t], z^′[t]}

In[276]:=

#''[t]  -#[t] & /@ var

Out[276]=

{x^′′[t]  -x[t], y^′′[t]  -y[t], z^′′[t]  -z[t]}

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