Hey guys! I would just like to ask if my partial differentiating is correct.

f(x,y)=xy (sin (4yx^2))
fyx = sin 4yx^2 + (8yx^2)(cos 4yx^2) + (12yx^2)(cos 4yx^2) - 32(x^4)(y^2)(sin 4yx^2)

Thanks!

Question

Hey guys! I would just like to ask if my partial differentiating is correct.

f(x,y)=xy (sin (4yx^2))
fyx = sin 4yx^2 + (8yx^2)(cos 4yx^2) + (12yx^2)(cos 4yx^2) - 32(x^4)(y^2)(sin 4yx^2)

Thanks!

ash2326 · Answer

You have differentiated with respect to x or y?

anonymous · Answer

Well, fyx. So I first diff with respect to y then with respect to x. :)

turingtest · Answer

it's the mixed derivative?
let me check...

ash2326 · Answer

Ok :)

turingtest · Answer

$$f_x=y\sin(4yx^2)+8x^2y^2\sin(4x^2y)\cos(4x^2y)$$I'm typing it out so we can all see if I make a mistake...

anonymous · Answer

Fy first. :) Then diff Fy with respect to x.

turingtest · Answer

the order shouldn't matter I don't think$$f_{xy}=\sin(4yx^2)+4yx^2\cos(4yx^2)+\frac{\partial}{\partial y}[8x^2y^2\sin(4x^2y)\cos(4x^2y)]$$

anonymous · Answer

Actually in some cases the order does not matter. But in others, it does. Anyway, thank you turing test! :)

turingtest · Answer

oh but I have a 16...

turingtest · Answer

I'll do it the other way on paper to see if that makes a diff

turingtest · Answer

ok I redid it the other way and got the same answer as you
sorry for the confusion

anonymous · Answer

It's okay Turing Test. I'm sorry for taking some of your time. :))) But, thanks again. I appreciate your effort.

turingtest · Answer

no it's my fault for messing up the first time
you're welcome