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Find the conditions for which a single-variable, real-valued function is differentiable

Contributed by:
Wolfram|Alpha Math Team

ResourceFunction["FunctionDifferentiability"][ returns the conditions for which | |

ResourceFunction["FunctionDifferentiability"][ returns the conditions for which | |

ResourceFunction["FunctionDifferentiability"][{ returns the conditions for which | |

ResourceFunction["FunctionDifferentiability"][{ returns the conditions for which | |

ResourceFunction["FunctionDifferentiability"][{{ ,…}},f_{2}x]returns the conditions for which the functions { ,…} are all differentiable with respect to f_{2}x. |

ResourceFunction["FunctionDifferentiability"] has the attribute HoldFirst.

ResourceFunction["FunctionDifferentiability"] takes only real-valued functions.

The constraint *cons* can be any logical combination of equations or inequalities:

lhs==rhs | equations |

lhs>rhs,lhs≥rhs,lhs<rhs,lhs≤rhs | inequalities (LessEqual,…) |

Compute the conditions for which a given function is differentiable:

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Compute the conditions for differentiability of a function subject to a constraint:

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A function that is differentiable for all real numbers returns True:

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The following function is once-differentiable everywhere but not twice-differentiable at *x*=0:

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FunctionDifferentiability has the attribute HoldFirst, enabling calculations such as the following:

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For a list of functions, FunctionDifferentiability returns the conditions for which all elements are differentiable:

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