- #1

#### trees and plants

- Homework Statement
- Test at every point ##(x_0, y_0) \in R^2 ## this function

##f(x,y) =\frac{x^3y}{x^6 + y^2}## if ##(x,y)\neq (0, 0)##,

##0## if ##(x, y) = (0, 0)##, for continuity, partial differentiability, differentiability, continuous partial differentiability and compute (where it exists) its derivative.

- Relevant Equations
- ##f(x,y) =\frac{x^3y}{x^6 + y^2}## if ##(x,y)\neq (0, 0)##,

##0## if ##(x, y) = (0, 0)##,

Perhaps use the definition of continuity, partial differentiability?