Taking the best linear approximation in a single direction determines a partial derivative, which is usually denoted ∂ y /∂ x.

Taking the time derivative yields the velocity of the particle:

Taking the derivative with respect to, and setting the result to zero and solving for, yields the Bose – Einstein population numbers:

Taking the derivative with respect to the proper time, we find the velocity component for μ = 0:

Taking the derivative with respect to time, this takes the more familiar form

Taking the derivative at t = 0, the associated differential operator ∇ must satisfy a product rule with respect to the metric:

Taking the Lie derivative of the relation then easily shows that

Taking the derivative of the adjoint map

Taking the derivative determines a linear map

Taking the derivative of strain with respect to time, we obtain:

Taking the derivative of H with respect to the p < sub > x </ sub > momentum component gives the formula

Taking in above expression outside the integral sign and expanding the integrand with the help of the Hadamard lemma one can obtain the following useful expression for the derivative of matrix exponent:

Taking averages of derivative payoffs at points in a low-discrepancy sequence is often more efficient than taking averages of payoffs at random points.

Taking the derivative of Hamilton's principal function S with respect to the conserved momentum p < sub > φ </ sub > yields

Taking an exterior derivative now shows

Taking the first derivative of the log-likelihood function

Taking the second derivative

Taking the first order derivative and equating it to zero ( for maximisation ) yields

Taking the derivative of P ( x ) with respect to, setting it to 0, and solving for x, we find that the optimal x is equal to 1 / e.

Taking the time derivative of the continuity equation and the spatial derivative of the force equation results in:

Taking a point in T < sub > x </ sub >* M is the same as choosing of a point x in M and a one-form ω at x, and the tautological one-form θ assigns to the point ( x, ω ) the value

The next limit ordinal above the first is ω + ω = ω · 2, and then we have ω · n, for any natural number n. Taking the union ( the supremum operation on any set of ordinals ) of all the ω · n, we get ω · ω = ω < sup > 2 </ sup >.

* Taking the Mystery out of the Infamous Formula ," SNR = 6. 02N + 1. 76dB ," and Why You Should Care.

Taking the Fourier transform ( unitary, angular frequency convention ) of a Gaussian function with parameters a, b = 0 and c yields another Gaussian function, with parameters ac, b = 0 and 1 / c.

Taking x =

Taking s = 2, we see that is equal to the sum of the reciprocals of the squares of the positive integers:

A simple example of a Butterworth filter is the third-order low-pass design shown in the figure on the right, with C < sub > 2 </ sub > = 4 / 3 F, R < sub > 4 </ sub > = 1 Ω, L < sub > 1 </ sub > = 3 / 2 H, and L < sub > 3 </ sub > = 1 / 2 H. Taking the impedance of the capacitors C to be 1 / Cs and the impedance of the inductors L to be Ls, where is the complex frequency, the circuit equations yield the transfer function for this device:

Taking n = 3, there are no degree 3 Kummer extensions of the rational number field Q, since for three cube roots of 1 complex numbers are required.

Taking = 288. 15 K,

Taking the s = 0 case, we have:

Taking X as the quotient space circle, we can regard the projection π from R = Y to X as a helix in geometrical terms, undergoing projection from three dimensions to the plane.

Taking an approach of Anekāntavāda, Ācārya Hemacandra is said to have displayed a broad-minded attitude, which pleased Kumarpal .< ref name = Hema >

He was the national leader of TCB Hate Crew ( TCB = " Taking Care of Business "), based in Texas with branches in Chicago and St. Louis, Missouri.

Taking advantage of liberalization by the unpopular ruling leftist / nationalist FLN regime, it used its preaching to advocate the establishment of a legal system following Sharia law, education in Arabic rather than French, and gender segregation, with women staying home to alleviate the high rate of unemployment among young Algerian men.

Taking a snapshot of an XFS filesystem involves freezing I / O to the filesystem using the utility, having the volume manager perform the actual snapshot, and then unfreezing I / O to resume normal operations.

Taking care of the units the radiation power for < sup > 60 </ sup > Co is 17. 9 W / g

Taking the Kyrgyz people as a representative example nomadism was the centre of their economy prior to Russian colonization at the turn of the C19 / C20, when they were settled into agricultural villages.

The audio and footage of this performance was included in the Taking Chances World Tour: The Concert CD / DVD.

* Mark Williams ( 1956-), controversial television, radio newspaper personality and a founding member of the National Association of Radio Talk Show Hosts / Tea Party Partriots / former chairman of the Tea Party Express, past President of the Conservative Party USA, author of " Exposing the Socialist Agenda " and " Taking Back America One Tea Party at a Time "

Taking a combined 29 % BCA / personal stake in Group Lotus, Wickins negotiated with the Inland Revenue, and then brought in new investors: merchant bank Schroeder-Wagg ( 14 %); Michael Ashcroft, Baron Ashcroft's Bermudan operating company Benor ( 14 %); Sir Anthony Bamford of JCB ( 12 %).

Taking 2 / 99 and 1 / 37, he did not secure a permanent place in the team until the 1928 series, where he took seventeen wickets, including 6 / 32 in the first innings of the first Test.

Taking an event with a 1 in 5 probability of occurring ( i. e. a probability of 1 / 5, 0. 2 or 20 %), then the odds are 0. 2 / ( 1 − 0. 2 )

Taking cultural context into consideration, the study still showed a positive correlation between empowerment and job satisfaction / commitment.

* Taking Back Sunday, a rock / alternative band

* 2007: Taking Care of Business ( double disc of Ride ' Til I Die ( w / 2 bonus tracks ) and 30th Anniversary Tour )

Health technology assessment ( HTA ): Taking responsibility for the physics component of health technology assessments related to medical radiological devices and / or the medical uses of radioactive substances / sources.

The film was later released on Blu-ray and DVD on May 4, 2010, along with the CD / DVD, Taking Chances World Tour: The Concert, which chronicled her world tour of the same name.

* Taking the Rough with the Smooch, LP / CD, 93, KILL ROCK STARS

Taking place near Königgrätz ( Hradec Králové ) and Sadowa ( Sadová ) in Bohemia on 3 July 1866, it was an example of battlefield concentration, a convergence of multiple units at the same location to trap and / or destroy an enemy force between them.

Taking advantage of the Database Kit to create a port for the Apache Derby database the ER / Box project provides an integrated all-Java, all open source Compiere distribution.

Taking the periods ( sums of roots of unity ) corresponding to these cosets applied to exp ( 2πi / p ), he notes that these periods have a multiplication table that is accessible to calculation.