Partial Derivatives, and Differentiable

[EV33]

Homework Statement

I want to show that the partials exist for a certain function.

Homework Equations

My book says that if a function f is differentiable at a point x then the partial derivatives exist.

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.

 

[Dick]

Homework Statement

I want to show that the partials exist for a certain function.

Homework Equations

My book says that if a function f is differentiable at a point x then the partial derivatives exist.

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.

Yes, to show the partials exists just use the limit definition. A function can fail to be differentiable and still have the partials exist.

 

[EV33]

Thank you for the help.