Analog Electronics
In a properly biased NPN transistor most of the electrons from the emitter

  are stopped by the junction barrier.
  pass through the base to the collector.
  recombine in the emitter its self.
  recombine with holes in the base .

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Analog Electronics
In an OP-amp differentiator

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

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