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  2. Total derivative - Wikipedia

    en.wikipedia.org/wiki/Total_derivative

    In many situations, this is the same as considering all partial derivatives simultaneously. The term "total derivative" is primarily used when f is a function of several variables, because when f is a function of a single variable, the total derivative is the same as the ordinary derivative of the function. [1]: 198–203

  3. Differential of a function - Wikipedia

    en.wikipedia.org/wiki/Differential_of_a_function

    A number of properties of the differential follow in a straightforward manner from the corresponding properties of the derivative, partial derivative, and total derivative. These include: [ 11 ] Linearity : For constants a and b and differentiable functions f and g , d ( a f + b g ) = a d f + b d g . {\displaystyle d(af+bg)=a\,df+b\,dg.}

  4. Category:Mathematical analysis - Wikipedia

    en.wikipedia.org/wiki/Category:Mathematical_analysis

    Shqip; සිංහල ... This category has the following 19 subcategories, out of 19 total. ... Total derivative; Total variation; Treatise on Analysis; U ...

  5. Derivative - Wikipedia

    en.wikipedia.org/wiki/Derivative

    The derivative of ′ is the second derivative, denoted as ⁠ ″ ⁠, and the derivative of ″ is the third derivative, denoted as ⁠ ‴ ⁠. By continuing this process, if it exists, the ⁠ n {\displaystyle n} ⁠ th derivative is the derivative of the ⁠ ( n − 1 ) {\displaystyle (n-1)} ⁠ th derivative or the derivative of order ...

  6. Exact differential equation - Wikipedia

    en.wikipedia.org/wiki/Exact_differential_equation

    Given a simply connected and open subset D of and two functions I and J which are continuous on D, an implicit first-order ordinary differential equation of the form (,) + (,) =,is called an exact differential equation if there exists a continuously differentiable function F, called the potential function, [1] [2] so that

  7. Fundamental increment lemma - Wikipedia

    en.wikipedia.org/wiki/Fundamental_increment_lemma

    In this case, M is the unique derivative (or total derivative, to distinguish from the directional and partial derivatives) of f at a. Notably, M is given by the Jacobian matrix of f evaluated at a. We can write the above equation in terms of the partial derivatives as

  8. Analytical mechanics - Wikipedia

    en.wikipedia.org/wiki/Analytical_mechanics

    If the kinetic energy is a homogeneous function of degree 2 of the generalized velocities, and the Lagrangian is explicitly time-independent, then: ((˙), (˙ ˙),) = ((˙), ˙ ˙,), (, ˙), where λ is a constant, then the Hamiltonian will be the total conserved energy, equal to the total kinetic and potential energies of the system: = + =.

  9. Generalizations of the derivative - Wikipedia

    en.wikipedia.org/wiki/Generalizations_of_the...

    The convective derivative takes into account changes due to time dependence and motion through space along a vector field, and is a special case of the total derivative. For vector-valued functions from R to R n (i.e., parametric curves ), the Fréchet derivative corresponds to taking the derivative of each component separately.