$$ z_x= (\cos x)(\sin y), \quad z_x= (\sin x)(\cos y). $$
Work Step by Step
Recall that $(\sin x)'=\cos x$. Since $ z= (\sin x)(\sin y) $, then we have $$ z_x= (\cos x)(\sin y), \quad z_x= (\sin x)(\cos y). $$
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