Question

If z is given implicitly as a function z=F(x,y), find derivatatie dz/dx when (x^3)+(y^3)+(z^3)=cos(x+y+z)..full question

Answer 1

treat \(y, z\) as if they were numbers (constants)

Answer 2

implicit differentiation

Answer 3

you cannot use "implicit differentiation" because you do not have an equation
in this case you cannot think of either \(y\) or \(z\) as functions of \(x\)