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Instead of taking the derivative of expression level with respect to time, we calculated the expression level derivative with respect to genomic position.
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Plasmid pPBHP92 is a derivative of the expression vector pTrcHisC (Invitrogen) that expresses the Sinorhizbium meliloti DctD AAA+ ATPase domain (E141-S390, DctD250ted DctD250) with an N-terminal 6x-His tag.
TSS prediction was based on the identification of abrupt changes in expression level as assessed by the approximation of the derivative of the expression level logarithm.
It can be shown that (R1)–(R4) is confluent and, hence, we are entitled to say: "Compute the derivative of an expression" (as opposed to simply "a" derivative).
After taking the derivative of the expression in (20) and equating to zero, we get: mathbf{widetilde{R}}_{bar{x}_{k}y_{k}}(n) mathbf{w}^{text{opt}}_{k}(n)= lambda mathbf{w}^{text{opt}}_{k}(n), (21).
(2) Assuming that are known, the observation is a linear function of and the optimum can easily be calculated with the derivative of the expression in brackets in (35) with respect to and setting the result to 0, yielding (36) which, from (29), yields.
The derivative of the expression in (4) is positive at τ=0 if ν σ 1 2 - σ 2 2 / 2 > k, i.e., if in laissez fair uninsurable idiosyncratic risk is the main reason why labor is not allocated to more productive uses.
Taking the derivative of above expression and using the Taylor series around A = 0, we have the LOD for ISS embedding as b ^ = sign ∑ i = 1 l 1 σ x i c ( l μ + 1 ) s i μ s i ∑ j ≠ i s j r j + ( 1 + μ ) r i ( c - 1 ) sign μ s i ∑ j ≠ i s j r j + ( 1 + μ ) r i. (50).
Her quotation was a derivative of an expression in Spanish " donde come uno comen dos," or "where one eats two eat" representing a cultural belief that even in times of food-related hardship there is always something to make to eat [ 57].
The YEp351 plasmid derivative for expression of the human HMG-CoA reductase was made in the following way.
On the other hand, derivatives of the expression in (3.25) with respect to x and t r respectively, are E m − 1, x ( μ j ( x, t r ), x, t r ) = − μ j, x ( x, t r ) ∏ k = 1 k ≠ j m − 1 ( μ j ( x, t r ) − μ k ( x, t r ) ), (3.35).
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com