Another question thrown at you

  • Thread starter precondition
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In summary, the conversation is about proving a mathematical equation involving a second order partial derivative. The participants discuss the function F(x,y) and its derivatives, as well as the use of the chain rule in solving the problem. The conversation ends with a request for help with the remaining questions.
  • #1
precondition
57
0
I think I'll get banned soon posting multiple questions at the same time, but allow me to continue,
if f,g:R-->R both of class C2(differentiable twice)
Define F(x,y)=f(x+g(y))
Show that (DxF)(DxDyF)=(DyF)(D^2xF) where D^2xF is second order partial derivative with respect to x
I'm dying here...
 
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  • #2
umm... forget it I think I can do this one.. lol
 
  • #3
Umm... I'm stuck..
 
  • #4
Rewrite [itex]F_x(x,y)[/itex] and [itex]F_{yx}(x,y)[/itex] in terms of derivatives of [itex]f(x+g(y))[/itex] and [itex]g(y)[/itex] (the rest is straightforward manipulation, using the chain rule).
 
  • #5
Yes! It did work! Thank you!
Now please the remaining questions I posted, could anyone please answer??
 

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