Analog Electronics
The voltage divider biasing circuit is used in amplifiers quite often because it

  reduces the DC base electric current.
  makes the operating point almost independent of β.
  reduces the cost of the circuit.
  limits the AC signal going to base.

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Analog Electronics
In an OP-amp differentiator

Polarity of input and output is the same
Output occurs when input is finite and constant
The amplitude of output is proportional to rate of change of input
The amplitude of output is proportional to input

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