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The map $f:A\\rightarrow B$ is called differentiable on the set $U\\subset A$, if at every point $x\\in U$ the increment of map $f$ can be represented as $$f(x+dx)-f(x) =\\frac{d f(x)}{d x}\\circ dx +o(dx)$$ where $$\\frac{d f(x)}{d x}:A\\rightarrow B$$ is linear map and $o:A\\rightarrow B$ is such continuous map that $$\\lim_{a\\rightarrow 0}\\frac{\\|o(a)\\|_B}{\\|a\\|_A}=0$$ Linear map $\\displaystyle\\frac{d f(x)}{d x}$ is called derivative of map $f$.\n  I considered differential forms in Banach Algebra. 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