- #1

lys04

- 70

- 3

- Homework Statement
- Picture

- Relevant Equations
- Partial derivatives

The ####x partial derivative is equal to $$L \frac{4x}{5(x^{2}+y^{2})^{\frac{-3}{5}}}$$ and the partial for ##y## is $$L \frac{4y}{5(x^{2}+y^{2})^{\frac{-3}{5}}}$$

Using the limit definition of partial derivatives I got the partial wrt ##x## is $$L \frac{h^{\frac{4}{5}}}{h}$$ which doesn’t exist as ##h## goes to ##0##. Similar argument for partial wrt ##y##. This means that ##f## isn’t ##C^1## at the origin, right?

At every other point the partial derivatives exist and is continuous because it’s a composition of a polynomial of two variables and ##x^2/5##, so ##f## is ##C^1## at all points except the origin.

Is the reasoning correct?

Using the limit definition of partial derivatives I got the partial wrt ##x## is $$L \frac{h^{\frac{4}{5}}}{h}$$ which doesn’t exist as ##h## goes to ##0##. Similar argument for partial wrt ##y##. This means that ##f## isn’t ##C^1## at the origin, right?

At every other point the partial derivatives exist and is continuous because it’s a composition of a polynomial of two variables and ##x^2/5##, so ##f## is ##C^1## at all points except the origin.

Is the reasoning correct?

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