Differentiator output
Wrap your neurons around these scope traces.  This should clear it up.

Then change all the generator properties to SIN.

Try a sawtooth.

Then drag and stretch the endpoints to make it an integrator but remember 5mm W. 


Finally.... LEDs are around 12 #Ohms @ 3.1V 20mA and not 3.1V/0.02A = 165 ohms avg when it comes to making a smooth turn on near full current.  That's# the Ri incremental impedance# of the zener-like diode response.