Analog Electronics
The extremely high input impedance of a MOSFET is primarily due to the

  absence of its channel.
  negative gate-source voltage.
  extremely small leakage electric current of its gate capacitor.
  depletion of electric current carriers.

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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
Polarity of input and output is the same
Output occurs when input is finite and constant

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