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Use the quotient rule to differentiate:

  1. f(x)=sec⁡(x)
  2. g(x)=\cosec(x)
  3. h(x)=cot⁡(x)

The value of

f′(π6)×g′(π4)×h′(π3)

can be given in simplest form as

pqr,p,q,r∈N

Give the value of pqr.