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Total derivative

| 🗖 nosplit | ↑ parent "Derivative" | words: 70
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The total derivative of a function assigns for every point of the domain a linear map with same domain, which is the best linear approximation to the function value around this point, i.e. the tangent plane.
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E.g. in 1D: $$Totalderivative=D[f(x0​)](x)=f(x0​)+∂x∂f​(x0​)×x (121)$$ and in 2D: $$D[f(x0​,y0​)](x,y)=f(x0​,y0​)+∂x∂f​(x0​,y0​)×x+∂y∂f​(x0​,y0​)×y (122)$$
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