$(Multi-$variable Differentiation$)*$

How many $of$ the following statements are true $in$ general?

$(a)\frac{de{l}^{2}f}{\text{d}\text{e}\text{l}\text{x}\text{d}\text{e}\text{l}\text{y}}=\frac{de{l}^{2}f}{\text{d}\text{e}\text{l}\text{y}\text{d}\text{e}\text{l}\text{x}}$

$(b)Iff$ has a local maximum $at(a,b)$ and $fis$ differentiable $at(a,b),$ then

gradf$(a,b)=(0,0).$

$(c)Iff(x,y)=lny,$ then gradf$(x,y)=\frac{1}{y}.$

$(d)If(3,2)is$ a critical point $off$ and then $f$

has a saddle point $at(3,2).$

$0$

$1$

$2$

$3$

$4$