I am learning the partial derivative and I am stuck on how to proceed with the following expression.
z = √(4 - x^2 - y^2)
the expressions I need to find are
Δ_x z,Δ_y z and Δz, which are are intersections in the plane x,y,z, where
Δ_x z = f(x+Δx,y) - f(x,y)
Δ_y z = f(x,y+Δy) - f(x,y)
Δz = f(x+Δx,y+Δy) - f(x,y)
I have been out of school for a few years now and I can't find any explanations on how to simplify addition expression in a radical such as the expresion z above and this is blocking me.
My first instinct would be to leave the expression complete (for example,
Δ_x z = √(4 - (x+Δx)^2 - y^2) - √(4 - x^2 - y^2), but in my previous examples, the
-f(x,y) part of the expressions would simplify the non-delta expressions and that confuses me.
Thank you for your help.