logarithmic differentiation

logarithmic differentiation

[′läg·ə‚rith·mik ‚dif·ə‚ren·chē′ā·shən]
(mathematics)
A technique often helpful in computing the derivatives of a differentiable function ƒ(x); set g (x) = log ƒ(x) where ƒ(x) ≠ 0, then g ′(x) = ƒ′(x)/ ƒ(x), and if there is some other way to find g ′(x), then one also finds ƒ′(x).
References in periodicals archive ?
By logarithmic differentiation of (3.4) and after some simplification, we have
Using the identities (2.5) and (2.17) in the logarithmic differentiation of (2.23) and simplifying the resulting equation, we get
With a focus on procedures for solving problems, rather than detailed explanations, the reader can whiz through chapters that illustrate derivatives, minimum-maximum problems, the chain rule, and logarithmic differentiation, among other facets of calculus.
Logarithmic differentiation of Equation 1 would again yield equations 28 and 37 in PB.
By Shephard's lemma, shadow-cost-minimizing input demand equations are derived by differentiating total shadow cost with respect to shadow prices, and therefore the observed quantities of inputs, [X.sub.i], are homogeneous of degree zero in shadow prices.(1) Similarly, logarithmic differentiation of the shadow cost function with respect to shadow prices yields the shadow cost shares, [Mathematical Expression Omitted], which are also homogeneous of degree zero in shadow prices.