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Field-Effect Transistor (FET) Transconductance

Transconductance (gmg_m) measures the change in drain current (IDI_D) with respect to the gate-source voltage (VGSV_{GS}), keeping the drain-source voltage (VDSV_{DS}) constant: gm=dIDdVGSg_m = \frac{\text{d}I_D}{\text{d}V_{GS}}.
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The statement of the theorem

The transconductance gmg_m quantifies the efficiency of voltage-to-current conversion in a FET. It is formally defined as the partial derivative of the drain current IDI_D with respect to the gate-source voltage VGSV_{GS}, while holding the drain-source voltage VDSV_{DS} constant: gm=∂ID∂VGS∣VDS=constg_m = \frac{\partial I_D}{\partial V_{GS}}\bigg|_{V_{DS} = \text{const}}.
Source: Wikipedia