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 with holes in the base .
  recombine in the emitter its self.

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Analog Electronics
In an OP-amp differentiator

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

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