Consider the surface defined by the equation x3 + y3 + z3 = 3xyz. Use implicit differ- ∂z entiation to find ∂x. (Note z is not actually a function of x and y here, but we can still find this partial derivative.)

Step-by-step explanation:

Given equation is ………………(1)

we use derivative formula

And also apply 'u v' formula

Differentiating  equation (1) partially with respective to 'x' , we treated 'y' as constant.

  ( here y treated as constant so the derivative of constant function is zero in addition but in multiplication the constant is keep as like 'y').

on simplification , we get

again simplification, we get

taking common ' on left on side , we get

dividing ' on both sides, we get

Final answer:-

answer: 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

step-by-step explanation: