F is a smooth function of x and y, i.e. F(x,y). If $H(x)=F(x,0)$, when can I have $\dfrac{\partial F}{\partial x}(x,0)= \dfrac{dH} {dx}(x)?$
I think we can show this equality from the definition of partial differentiation easily. Is this equality true for all functions of (x,y) which are first order differentiable with respect to x?
Thanks