Thread: Total Differential Problem

Hi

I am trying to get the total differential for

y = x₁x₂/2x₁ + x₂

I have been given the answer

dy = [x₂/2x₁ + x₂]dx₁ - [2x₁x₂/(2x₁+x₂)^2]dx₁ + [x₁/2x₁ + x₂]dx₂ - [x₁x₂/(2x₁+x₂)^2]dx₂

Is this right?

It is my understanding that the general formula is F₁dx₁ + F₂dx₂, for y=F(x₁,x₂)

I don't understand why, in the second and fourth terms of the answer, the WHOLE of the denominator is being squared, rather than just the x₁ or x₂ that the partial derivative refers to......

Originally Posted by econolondon

Hi

I am trying to get the total differential for

y = x₁x₂/2x₁ + x₂

I have been given the answer

dy = [x₂/2x₁ + x₂]dx₁ - [2x₁x₂/(2x₁+x₂)^2]dx₁ + [x₁/2x₁ + x₂]dx₂ - [x₁x₂/(2x₁+x₂)^2]dx₂

Is this right?

It is my understanding that the general formula is F₁dx₁ + F₂dx₂, for y=F(x₁,x₂)

I don't understand why, in the second and fourth terms of the answer, the WHOLE of the denominator is being squared, rather than just the x₁ or x₂ that the partial derivative refers to......

1. I assume that your function reads:

2. You have to use the quotient rule:

3. I'll show you the part:

The variable is . is considered to be constant.



4. The part has to be done in excatly the same way.

Thanks, that's very helpful.