Suppose the equation F(x,y,z) = 𝑥^2 +𝑦^2 − 2𝑧^2 +12x −8z – 4 = 0 can be solved for z as z = f(x,y). Find 𝜕z/𝜕x at the point P(1,1,1). Use implicit dif f differentiation.

Question

Suppose the equation F(x,y,z) = 𝑥^2 +𝑦^2 − 2𝑧^2 +12x −8z – 4 = 0 can be solved for  z as z = f(x,y).            Find 𝜕z/𝜕x at the point P(1,1,1). Use implicit dif f differentiation.

oobleck · Answer

what's the trouble? 2x - 4z 𝜕z/𝜕x + 12 - 8 𝜕z/𝜕x = 0 Now just solve for 𝜕z/𝜕x

Anonymous · Answer

Why are you taking the derivative of both z and x at the same time? Are you making a mistake? I thought the problem meant partial derivative of z over partial derivative of x then plug in and solve. Am I right?