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Please find fxy?

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1 Answer

Well...if you are referring to: ∂2f/(∂y∂x) then you just take the partial derivatives one at a time:

First use the product rule:

∂f/∂x = ∂/∂x[  (xy) * (e^(x2y)) ] = ∂/∂x[xy]*(e^(x2y)) + ∂/∂x[e^(x2y)]*(xy)

= ye^(x2y) + 2xye^(x2y)(xy) = e^(x2y) * (y + 2x2y2)

 

Then do the same process to ∂f/∂x, this time taking the partial derivative with respect to y:

 

2f/(∂y∂x) = ∂/∂y[ ∂f/∂x ] = ∂/∂y [ e^(x2y) * (y + 2x2y2) ] = ∂/∂y[ e^(x2y) ] * (y +2x2y2)    +  ∂/∂y[ y + 2x2y2 ] * e^(x2y)

= e^(x2y)*x2*(y+2x2y2) + (1+4x2y)*e^(x2y) = e^(x2y) * (x2y + 2x4y2 + 1 +4x2y) = e^(x2y) * (2x4y2 + 5x2y + 1)