How many partial derivatives of order 3 are for a function of 3 variables?

C. (3,0)

Step-by-step explanation:

Since both of the equations in this system have y equal to something else, we know that those two parts are equal. For example y=x-3, but y also equals x^2-5x+6. This means that x-3=x^2-5x+6. Now we can solve this equation for x.

First you subtract x on both sides to get -3=x^2-6x+6. Then, you add 3 to both sides to get 0=x^2-6x+9. Now we can factor x^2-6x+9 into (x-3)^2. This means that (x-3)^2=0. Now we can use the Zero Product Property to find out whta x equals. Since (x-3) is repeated twice, we can say x-3 must equal 0 as otherwise the whole equation would be wrong. This means x-3=0 or x=3. Now since x can only equal 3, the answer must be C.