Inductor as a differentiator (op amp)

[jesuslovesu]

Homework Statement

Sorry this computer doesn't have access to PSPICE and I don't have a scanner, but let's say that I have an op amp.
1) there is a time varying voltage source Vs
2) There is a resistor R1 connected to the inverting input of the op amp
3) The noninverting pin is connected to ground
4) There is an inductor connected from the inverting pin to the output of the op amp where there is also + - Vout represented.

How does one do the nodal equations to verify that this configuration is a differentiator?

Homework Equations

The Attempt at a Solution

I came up with (0 - Vs) / R + i(t) = 0
Vs / R = i(t)
I know vL = L di/dt
but wouldn't that be an integrator if I wanted to solve for i?

I don't see how this would be a differentiator

 

[anorlunda]

I came up with (0 - Vs) / R + i(t) = 0

That can't be right. There is no L in that equation.