analysis, the logarithmic derivative of a function f is defined by the formula f ′ f {\displaystyle {\frac {f'}{f}}} where f′ is the derivative of f. Intuitively...

The symmetric logarithmic derivative is an important quantity in quantum metrology, and is related to the quantum Fisher information. Let ρ {\displaystyle...

calculus, logarithmic differentiation or differentiation by taking logarithms is a method used to differentiate functions by employing the logarithmic derivative...

hand side is called the logarithmic derivative of f. Computing f'(x) by means of the derivative of ln(f(x)) is known as logarithmic differentiation. The...

}}f_{i<n}(x)>0{\text{ and }}{\frac {df_{i}}{dx}}{\text{ exists.}}} The logarithmic derivative is another way of stating the rule for differentiating the logarithm...

logarithmic derivative provides a simpler expression of the last form, as well as a direct proof that does not involve any recursion. The logarithmic...

) | {\displaystyle \ln |h(x)|=\ln |f(x)|-\ln |g(x)|} Taking the logarithmic derivative of both sides, h ′ ( x ) h ( x ) = f ′ ( x ) f ( x ) − g ′ ( x )...

decomposition of cot ⁡ z {\displaystyle \cot z} given above, which is the logarithmic derivative of sin ⁡ z {\displaystyle \sin z} . From this, it can be deduced...

… {\displaystyle 0,0,1,1,4,1,5,1,12,6,7,1,16,1,9,\ldots } The logarithmic derivative ld ⁡ ( x ) = D ( x ) x = ∑ p ∈ P p ∣ x ν p ( x ) p {\displaystyle...

{n}{m}}\right)=(-1)^{(m-1)(n-1)/4}.} Let D(n) be the arithmetic derivative. Then the logarithmic derivative D ( n ) n = ∑ p  prime p ∣ n v p ( n ) p . {\displaystyle...

}^{2}} , where L ϱ {\displaystyle L_{\varrho }} is the symmetric logarithmic derivative For a unitary encoding operation ϱ ( θ ) = exp ⁡ ( − i A θ ) ϱ 0...

the logarithmic derivative of f {\displaystyle f} , which is ( log ⁡ f ) ′ = f ′ / f {\displaystyle (\log f)'=f'/f} , and the logarithmic derivative of...

In mathematics, the digamma function is defined as the logarithmic derivative of the gamma function: ψ ( z ) = d d z ln ⁡ Γ ( z ) = Γ ′ ( z ) Γ ( z ) ...

cotangent, and squared cosecant functions: the logarithmic derivative of the sine is the cotangent, whose derivative is negative the squared cosecant. The Weierstrass...

distribution Logarithmic algorithm Logarithmic convolution Logarithmic decrement Logarithmic derivative Logarithmic differential Logarithmic differentiation...

\end{aligned}}} Where the digamma function ψ(α) is defined as the logarithmic derivative of the gamma function: ψ ( α ) = d ln ⁡ Γ ( α ) d α {\displaystyle...

A logarithmic spiral, equiangular spiral, or growth spiral is a self-similar spiral curve that often appears in nature. The first to describe a logarithmic...

theorem L'Hôpital's rule General Leibniz rule Mean value theorem Logarithmic derivative Differential (calculus) Related rates Regiomontanus' angle maximization...

a meromorphic function to a contour integral of the function's logarithmic derivative. If f is a meromorphic function inside and on some closed contour...

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...

equal to c. This statement can be applied in particular to the logarithmic derivative of Riemann zeta function, and thus provides an extremely short way...

function of several variables is the matrix of all its first-order partial derivatives. If this matrix is square, that is, if the number of variables equals...

directional derivative measures the rate at which a function changes in a particular direction at a given point.[citation needed] The directional derivative of...

where ψ ( z ) {\displaystyle \psi (z)} is the digamma function, the logarithmic derivative of the gamma function. There is also a corresponding integral formula...

coefficients in the finite field Fq is defined as a function whose logarithmic derivative generates the number Nk of solutions of the equation defining V...

sensitivity measure, defined as the percentage derivative of price with respect to yield (the logarithmic derivative of bond price with respect to yield). Modified...

of the derivative Fractal derivative – Generalization of derivative to fractals Hasse derivative – Mathematical concept Logarithmic derivative – Mathematical...

{\displaystyle ={\frac {d}{dt}}\ln {\bigl (}a(t){\bigr )}} This is the logarithmic derivative of the accumulation function. Conversely: a ( t ) = e ∫ 0 t δ s...

especially over spaces of matrices. It collects the various partial derivatives of a single function with respect to many variables, and/or of a multivariate...

the exterior derivative extends the concept of the differential of a function to differential forms of higher degree. The exterior derivative was first described...