# Partial derivative of bivariate cdf

Suppose the bivariate cdf $$F(a,b)=Pr(X\leq a, Y\leq b)$$ is differentiable in $$(a,b)$$. Is it true that $$\frac{\partial Pr(X\leq a, Y\leq b)}{\partial a}=Pr(X=a,Y\leq b)$$?

• Would you need to ask this question if the "$,Y\le b$" references were dropped? If not, then consider how their appearance possibly could change the answer. – whuber Mar 2 '20 at 20:20
• Thanks a lot. This makes it clear. – T34driver Mar 3 '20 at 0:38