# Total differential Problem

1. May 29, 2016

### Nanu Nana

1. The problem statement, all variables and given/known data
You have two parameters x = 12 and y = 3 set on a machine. The machine generates a function: z (x, y) = 3sin (x ^ 2 + y) y + x ^ 3
Use the total differential of this function in the set point to determine which of the parameters to be set to the most accurate.
2. Relevant equations
dz = (∂z/∂x) dx + (∂z/∂y) dy
3.Solution
z = 3y sin(x²+y) + x^3

dz = (3y cos(x²+y) * 2x + 3x²) dx + (3 sin(x²+y) + 3y cos(x²+y) * 1 + 0) dy
dz = (6xy cos(x²+y) + 3x²) dx + (3 sin(x²+y) + 3y cos(x²+y)) dy

I don't understand why (∂z/∂y) = (3 sin(x²+y) + 3y cos(x²+y) * 1 + 0) dy Where did that zero came from ??? and 1 ??

2. May 29, 2016

### BvU

So, NN, where is your attempt at solution ?
What would be your $\partial z\over \partial y$ ?

3. May 29, 2016

### Megaquark

Writing he zero is kind of unnecessary, but it comes from taking the partial derivative of x3 with respect to y. The 1 comes from the y...chain rule.

4. May 29, 2016

### BvU

Did you notice the posting in 'homework' ? It is not good for the poster and it is against PF rules to give such a direct answer: it robs the poster from an opportunity to learn from insight.

5. May 29, 2016

### Nanu Nana

(3 sin(x²+y) + 3y cos(x²+y) * 1 + 0) dy

6. May 29, 2016

### Nanu Nana

Oh I see, thank you very much

7. May 29, 2016

### Megaquark

You're welcome.

8. May 29, 2016

### Megaquark

Nope, I didn't notice. I'll likely avoid answering posts in this section from now on.