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F(x,y) and y=y(t) and x=x(t)

Therefore,

F

_{t}= F

_{x}*x

_{t}+ F

_{y}*y

_{t}. Right?

Can I write

F

_{tt}= (F

_{xx}*x

_{t}+ F

_{yy}*y

_{t})*x

_{t}+ F

_{x}*x

_{tt}+ (F

_{xx}*x

_{t}+ F

_{yy}*y

_{t})*y

_{t}+ F

_{y}*y

_{tt}

?

Basically I'm trying to figure out the second derivative by chain rule.