1. The problem statement, all variables and given/known data I want to show that the partials exist for a certain function. 2. Relevant equations My book says that if a function f is differentiable at a point x then the partial derivatives exist. 3. The attempt at a solution Rather than showing f is differentiable, I am curious if it is sufficient to just use the limit definition of a partial derivative and show that the limit exists? Thank you for your time.