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Your likelihood is $$P(w_t\mid h) = \frac{\exp(s_\theta(w_t,h))}{\sum_{w'\in V} \exp(s_\theta (w', h))}.$$ $w_t$ is one specific value, while $w'$ is the index of the sum, and it's taking on all values in $V$. Then you take the log of this, then the derivative. In the second part of your derivation, you're only looking at the second term, which came from ...