Para encontrar a derivada parcial, realizaremos os cálculos abaixo:

\(\begin{align} & f(x)=2-{{x}^{2}} \\ & f'({{2}^{-}})=\underset{x\to 0}{\mathop{\lim }}\,\frac{-2-{{(x+2)}^{2}}-2-{{(-2)}^{2}}}{x} \\ & f'({{2}^{-}})=\underset{x\to 0}{\mathop{\lim }}\,\frac{-2-{{(x+2)}^{2}}-6}{x} \\ & f'({{2}^{-}})=\underset{x\to 0}{\mathop{\lim }}\,\frac{-{{(x+2)}^{2}}-8}{x} \\ & f'({{2}^{-}})=\underset{x\to 0}{\mathop{\lim }}\,\frac{{{x}^{2}}+4x+4-8}{x} \\ & f'({{2}^{-}})=\underset{x\to 0}{\mathop{\lim }}\,\frac{{{x}^{2}}+4x-4}{x} \\ & f'({{2}^{-}})=\frac{4+8-4}{2} \\ & f'({{2}^{-}})=4 \\ \end{align} \)

Portanto, a derivada parcial da função dada será \(\boxed4\).