Let $g ( x , y ) = \left( x ^ { 2 } + y ^ { 2 } \right) f ( x , y )$ , where $f ( x , y ) = \left\{ \begin{array} { l l }
- | y | & | y | \leq | x | \
- | x | & | x | \leq | y |
\end{array} \right.$ g is differentiable at (0,0).

Question

Let $g ( x , y ) = \left( x ^ { 2 } + y ^ { 2 } \right) f ( x , y )$ , where $f ( x , y ) = \left\{ \begin{array} { l l } 
- | y | & | y | \leq | x | \
- | x | & | x | \leq | y |
\end{array} \right.$ g is differentiable at (0,0).

Quizplus · Accepted Answer

g is differentiable at (0,0) because f is continuous at (0,0) and g is the product of two differentiable functions.

Let g(x,y)=(x2+y2)f(x,y)g ( x , y ) = \left( x ^ { 2 } + y ^ { 2 } \right) f ( x , y )g(x,y)=(x2+y2)f(x,y)

Let $g ( x , y ) = \left( x ^ { 2 } + y ^ { 2 } \right) f ( x , y )$