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Differentiable function - Wikipedia
https://en.m.wikipedia.org/wiki/Differentiable_function
WEBIn mathematics, a differentiable function of one real variable is a function whose derivative exists at each point in its domain. In other words, the graph of a differentiable function has a non- vertical tangent line at each interior point in its domain.
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Differentiable - Math is Fun
https://www.mathsisfun.com/calculus/differentiable.html
WEBDifferentiable means that the derivative exists ... Example: is x 2 + 6x differentiable? Derivative rules tell us the derivative of x 2 is 2x and the derivative of x is 1, so: Its derivative is 2x + 6. So yes! x 2 + 6x is differentiable. ... and it must exist for every value in the function's domain. Example (continued)
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Differentiable - Formula, Rules, Examples - Cuemath
https://www.cuemath.com/calculus/differentiable/
WEBA differentiable function is a function in one variable in calculus such that its derivative exists at each point in its entire domain. How to Prove a Function is Differentiable? A function can be proved differentiable if its left-hand limit is equal to the right-hand limit and the derivative exists at each interior point of the domain.
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Differentiable Function | Brilliant Math & Science Wiki
https://brilliant.org/wiki/differentiable-function/
WEBIn calculus, a differentiable function is a continuous function whose derivative exists at all points on its domain. That is, the graph of a differentiable function must have a (non-vertical) tangent line at each point in its domain, be relatively "smooth" (but not necessarily mathematically smooth), and cannot contain any breaks, corners, or ...
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3.2: The Derivative as a Function - Mathematics LibreTexts
https://math.libretexts.org/Bookshelves/Calculus/Calculus_(OpenStax)/03%3A_Derivatives/3.02%3A_The_Derivative_as_a_Function
WEBA function \(f(x)\) is said to be differentiable at \(a\) if \(f'(a)\) exists. More generally, a function is said to be differentiable on \(S\) if it is differentiable at every point in an open set \(S\), and a differentiable function is one in which \(f'(x)\) exists on its domain.
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