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Assume that and are differentiable on T with.
Let be two continuous functions which are differentiable on.
Let f, g : [ a, b ] → R be two continuous functions which are differentiable on ( a, b ).
Lemma 1. ([[2 5], A Monotone form of L'Hospital's rule]) Let f, g : [a, b] → ℝ be two continuous functions which are differentiable on (a, b).
Suppose that (f x,y)), (g x,y)), (h x,y)) and (v x,y)) are differentiable on ((-infty, +infty times -infty,+infty times -infty
For (-infty < a< bare differentiable on (( a,b ) ), with (f ( a ) =g ( a ) =0) or (f ( b ) =g ( b ) =0).
Similar(53)
The idea is to embed the continuous functions in a larger space called the space of distributions and only require that a function is differentiable "on average".
If is differentiable on then is differentiable on, with.
Let be differentiable on and continuous on.
Let and be differentiable on time scale with for all.
If is differentiable on, then is Schur-convex on if and only if (16).
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com