The constant is the initial velocity term that would be lost upon taking the derivative of velocity because the derivative of a constant term is zero.

In the Lagrangian description, the material derivative of is simply the partial derivative with respect to time, and the position vector is held constant as it does not change with time.

This model may not have a constant derivative.

The derivative of x is the constant function with value 1, and the derivative of f ( g ( x )) is determined by the chain rule.

The present IUPAC definition is that affinity A is the negative partial derivative of Gibbs free energy G with respect to extent of reaction ξ at constant pressure and temperature.

Since the rate of clocks and the gravitational potential have the same derivative, they are the same up to a constant.

For positive integer m the derivative of gamma function can be calculated as follows ( here γ is the Euler – Mascheroni constant ):

It is not an argument of the function, and will, for instance, be a constant when considering the derivative.

Assuming that the masses are constant, the virial G is one-half the time derivative of this moment of inertia

* The function f ( x ) = defined for all real numbers is Lipschitz continuous with the Lipschitz constant K = 1, because it is everywhere differentiable and the absolute value of the derivative is bounded above by 1.

Its derivative is essentially bounded in magnitude by the Lipschitz constant, and for a < b, the difference g ( b ) − g ( a ) is equal to the integral of the derivative g ′ on the interval.

Moreover, if K is the best Lipschitz constant of ƒ, then whenever the total derivative Dƒ exists.

In mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constant ( as opposed to the total derivative, in which all variables are allowed to vary ).

By finding the derivative of the equation while assuming that y is a constant, the slope of ƒ at the point is found to be:

In this expression, a is a constant, not a variable, so f < sub > a </ sub > is a function of only one real variable, that being y. Consequently, the definition of the derivative for a function of one variable applies:

In fields such as statistical mechanics, the partial derivative of f with respect to x, holding y and z constant, is often expressed as

The minimum total potential energy is found by taking the derivative with respect to H and equating to zero.

Countries where ASL or a derivative of ASL is the national or a widespread language include Barbados, Belize, Benin, Bolivia, Botswana ( with BSL ), Burkina Faso, Burundi, Cameroon, Canada, the Central African Republic, Chad, Côte d ' Ivoire, the Democratic Republic of the Congo, the Dominican Republic, El Salvador, Gabon, Gambia, Ghana, Guinea, Guyana, Haiti, Honduras, Jamaica, Kenya ( minority use ), Liberia, Madagascar ( minority use ), Mali, Mauritania, Niger, Nigeria, Philippines ( L2 use ), Puerto Rico, Senegal, Sierra Leone, Trinidad and Tobago, Togo, and Zimbabwe ( with ZSL ).

Dante concludes ( Paradiso XXVI ) that Hebrew is a derivative of the language of Adam.

Today, his descendants can be found in many places outside of Afghanistan, such as in America, France, Germany, and even in Scandinavian countries such as Denmark and carry the surname of Ziyaee, which is itself a derivative of the King's title.

* Conservation of Momentum: This equation applies Newton's second law of motion to a continuum, whereby force is equal to the time derivative of momentum.

The expression on the left side is a material derivative.

of a function f is a differentiable function F whose derivative is equal to f, i. e., F ′ = f. The process of solving for antiderivatives is called antidifferentiation ( or indefinite integration ) and its opposite operation is called differentiation, which is the process of finding a derivative.

The time derivative of angular momentum is called torque:

The torque caused by the two opposing forces F < sub > g </ sub > and-F < sub > g </ sub > causes a change in the angular momentum L in the direction of that torque ( since torque is the time derivative of angular momentum ).

* Tofisopam ( Emandaxin and Grandaxin ) is a drug that is a benzodiazepine derivative.

A stationary point is a geometry such that the derivative of the energy with respect to all displacements of the nuclei is zero.

If we attempt to use the above formula to compute the derivative of f at zero, then we must evaluate 1 / g ′( f ( 0 )).

Note derivative is positive number | positive where green line appears, negative number | negative where red line appears, and zero ( number ) | zero where black line appears.

or, equivalently, the Wirtinger derivative of ƒ with respect to the complex conjugate of z is zero:

In regions where the first derivative is not zero, holomorphic functions are conformal in the sense that they preserve angles and the shape ( but not size ) of small figures.

This bilinear operation is actually the zero map, but the second derivative, under the proper identification of tangent spaces, yields an operation that satisfies the axioms of a Lie bracket, and it is equal to twice the one defined through left-invariant vector fields.

To find the runner speed at maximum power, take the derivative of P with respect to u and set it equal to zero, 2ρQ ( V < sub > i </ sub > − 2u ).

The closed condition means that the exterior derivative of ω, namely dω, is identically zero.

Note derivative is positive number | positive where green, negative number | negative where red, and zero ( number ) | zero where black

In some mathematical contexts, zero-based numbering can be used without confusion, when ordinal forms have well established meaning with an obvious candidate to come before first ; for instance a zeroth derivative of a function is the function itself, obtained by differentiating zero times.

Using a uniqueness theorem and showing that a potential satisfies Laplace's equation ( second derivative of V should be zero i. e. in free space ) and the potential has the correct values at the boundaries, the potential is then uniquely defined.

The main problem with the central difference method, however, is that oscillating functions can yield zero derivative.

Differentiating u ( λ, T ) with respect to λ and setting the derivative equal to zero gives

If f is a differentiable function on R ( or an open interval ) and x is a local maximum or a local minimum of f, then the derivative of f at x is zero ; points where are called critical points or stationary points ( and the value of f at x is called a critical value ).

For instance, suppose that f has derivative equal to zero at each point.

* there exists a set N of measure 0 such that for all x outside of N the derivative ƒ ′( x ) exists and is zero, that is, the derivative of f vanishes almost everywhere.

These include the ferromagnetic phase transition in materials such as iron, where the magnetization, which is the first derivative of the free energy with respect to the applied magnetic field strength, increases continuously from zero as the temperature is lowered below the Curie temperature.

The derivative of the function f has a zero where the maximal eccentricity is attained.