calculus question

eoins23456

f(x; y) = (x - 1)(y -2)(x + y)
Calculate fx; fy; fxx; fyy; fxy

anyone know how to do this?
Im guessing the first one is just get x on its own,then get y on its own for the second one.how bout the next three?just the method now the actual answer please thanks!

LeixlipRed

This involves the differentiation of functions with more than one variable, two in this case. The method is called partial differentiation. You can see a bit about that here.

The first thing you need to do is calculate the first-order derivatives, those are [latex]f_{x}[/latex] and [latex]f_y[/latex]. To calculate [latex]f_{x}[/latex] you differentiate f with respect to x and hold y constant. i.e. you just differentiate x as you normally would and treat y as if it were a constant. Then for [latex]f_y[/latex] you do the opposite, differentiate w.r.t y and hold x constant.

An example would be if f(x,y)=2xy then [latex]f_x[/latex] would be 2y and [latex]f_y[/latex] would be 2x. Try the first order ones first and worry about the others after.

sponsoredwalk

I'll assume that fx is notation for the partial derivative with respect to x.
Well in f(x,y) what you could do is multiply the whole thing out & then
take the derivative w.r.t. x holding y constant etc...

The notation fyy would be better written as (fx)y which is just saying that
you should take the partial derivative of (fx) w.r.t. y. If (fx) = Q then we
can write (fx)y = Qy. You get what I'm saying hopefully Basically just
take the partial derivative with respect to y of the partial derivative with
respect to x of f(x,y). Another way to say this is that you just take the
partial derivative with respect to y of the partial derivative of f(x,y) with
respect to x. You could also use thee product rule on this if you wanted,
instead of multiplying it all out.

edit: Didn't see Red respond, I was 2 minutes too slow!

bnt

I see they've asked you to calcuate [latex]f_{xy}[/latex] but not [latex]f_{yx}[/latex], which is probably because they should both give the same result. If you're new to this I suggest you do both anyway, and if they're different, something's gone Wrong somewhere.