## The total differential

Determine whether the given functions have a total differential at the point $$(x, y) = (0, 0)$$ and write down the associated coefficients.

• #### Variant 1

$$(1 + x)^k (1 + y)^{\ell}$$, where $$k, \ell \in \mathbb N$$ are parameters.

• #### Variant 2

$$\ln (1 + x) \ln (1 + y)$$

• #### Variant 3

$$(1 + x)^{1 + y}$$