Find the first partial derivatives ∂z/∂x and ∂z/∂y of sin(0x+5y+z)=0 at (0,0,0).
The Attempt at a Solution
∂z/∂x= 0 and ∂z/∂y= -5
What I do not understand is WHY 0x+5y+z=kπ is an acceptable equation. I found it from a solution of this online, but with no explanation. What is the significance of k and π, and why can we basically ignore the sin?