How to compute Vds for this MOSFET transistor
If this is a DC analysis, then you can ignore all of the nets with capacitors, and you end up with essentially a voltage divider made up of R\$_{G2}\$, R\$_{G1}\$, R\$_{GD}\$, and R\$_{D}\$.

R\$_{DS}\$ is the resistance between the drain and source; when the MOSFET is off, it is very high, when the MOSFET is on, or saturated, it is very low, the maximum value is generally given in a datasheet as R\$_{DS}\$(on).

The voltage at the drain is then:

$$V_{d} = V_{dd} \space\times\space \frac{R_{D}}{(\frac{(R_{G2}+R_{G1}+R_{GD})\space\times\space R_{DS}}{R_{G2}+R_{G1}+R_{GD}+R_{DS}})}$$

Since the voltage at the source is V\$_{dd}\$, then the voltage V\$_{sd}\$ is:

$$V_{sd} =  V_{dd} - (V_{dd} \space\times\space \frac{R_{D}}{(\frac{(R_{G2}+R_{G1}+R_{GD})\space\times\space R_{DS}}{R_{G2}+R_{G1}+R_{GD}+R_{DS}})})$$

$$          \space =  V_{dd} \space\times\space (1 - \frac{R_{D}}{(\frac{(R_{G2}+R_{G1}+R_{GD})\space\times\space R_{DS}}{R_{G2}+R_{G1}+R_{GD}+R_{DS}})})$$