MathCastle
Multivariable CalculusChallengePartial Derivatives & the Gradient

Partial Derivatives & the Gradient · Challenge problem

The equation x2+y2+z2+xyz=4x^2 + y^2 + z^2 + xyz = 4 defines zz implicitly near (1,1,1)(1, 1, 1). Compute ∂z∂x\dfrac{\partial z}{\partial x} at that point.