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# Respond with true or false to the following assertion. Be prepared to defend your answer.If $f_x\left(x_0, y_0\right)$ and $f_y\left(x_0, y_0\right)$ both exist, then $f$ is differentiable at $\left(x_0, y_0\right)$.

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Given if$f_{x}\left( x_{0},y_{0}\right)$ and $f_{y}\left( x_{0},y_{0}\right)$ both exist but are not continuous,therefore the function $f\left( x,y\right)$ is not differentiable at $\left( x_{0},y_{0}\right)$ ,then false

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