Find the partial derivatives of f(x,y) = x^2 -x*y +(y^2)/(2) +3 with respect to x and y. The partial derivative of f(x,y) wrt x would be 2x-y+(y^2)/(2) and the partial derivative of f(x,y) wrt y would be x^2 -x+y?

Question

ganeshie8 · Answer

when differentiating wrt x, you treat y as constat

ganeshie8 · Answer

when u differentiate wrt x, there is not much difference between 3 and y

ganeshie8 · Answer

f(x,y) = x^2 -x*y +(y^2)/(2) +3

wrt x would be 2x - y + 0 + 0

tiffany_rhodes · Answer

Oh okay, so if y is by itself as in the case (y^2)/(2), you keep it constant and the derivative of a constant is just 0.

tiffany_rhodes · Answer

I don't know why I took the derivative of that. My bad.

ganeshie8 · Answer

thats right

tiffany_rhodes · Answer

Thanks for the clarification!

ganeshie8 · Answer

here is a nice graph http://moodle.capilanou.ca/pluginfile.php?file=/457165/mod_book/chapter/1398/x_derivative.JPG

dan815 · Answer

yes very good

dan815 · Answer

u must think about it like this
F_x is how the slope of this function changes as a function y, when y is varied along, how is the function changing with respect to x

tiffany_rhodes · Answer

great! I always have a difficult time trying to visualize these graphs in 3D so this helps!

ganeshie8 · Answer

notice that $\large \dfrac{\partial}{\partial x}f(x,y)$ represents the slope of tangent of cross section curve formed when you intersect a vertical plane y = k with the funciton f(x,y)

dan815 · Answer

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