derivative - the result of mathematical differentiation; the instantaneous change of one quantity relative to another; df(x)/dx derived function, differential, differential coefficient, first derivative curvature - the rate of change (at a point) of the angle between a curve and a tangent to the...
Differential equation relates a function with its derivative. The n-th derivative is of the form {eq}f^{n} (x) = \dfrac{\ d^n f}{\ dx^n} {/eq}. There are many techniques to find the derivative of a function. In this problem, we need to compute the third derivative of the ...
Journal of Knot Theory & Its RamificationsMiyazawa Y. The third derivative of the Jones polynomial[J].Journal of Knot Theory and Its Ramifications 1997,6.Miyazawa,Y.The third derivative of the Jones polynomial. J. Knot Theory Ramifications . 1997...
Find the first, second, and third derivative for sinx2−cosx2 . Chain Rule And Product Rule: The derivatives of composite functions of several variables are calculated by chain rule. For a function f(g(x)), the chain rule is given by f(g(x))′=f′(g(x))g′(x...
In contrast to case (iv) above, already with four points on a three-factor Segre spanning a three-dimensional vector space, one can obtain new limits by taking a second derivative, even when the limiting points are distinct. Consider the points x 1=a 1⊗b 1⊗c 1, x 2=a 2⊗b...
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**Problem Statement:** Find the function \( f(x) \). **Given:** - The third derivative of \( f \), denoted as \( f'''(x) \), is given by: \[ f'''(x) = x^{-2} \] - The domain is specified as \( x > 0 \). **Initial Conditions:** - \( f(1)...
An important consequence of the Third Law is that it denies the existence of an ideal gas. For, as we establish in Chapter 2, its entropy is given by (1.18.7)S=CVlnT+RlnV, whose derivative, (∂S/∂V)T = R/V does not vanish at T = 0. This fact, of course, does not pre...
In this study the following second-order radial derivative for the Earth’s disturbance potential Trr is adopted23: Trr(r,θ,λ)=GMR3∑l=2∞(l+1)(l+2)(Rr)l+3×∑m=0l(C¯lmcosmλ+S¯lmsinmλ)P¯lm(cosθλ) (7) where (r,θ,λ) are the geocentric spherica...
PERIODIC SOLUTIONS OF THE THIRD–ORDER DIFFERENTIAL EQUATION x′′′ + x′ + εF (t, x, x′, x′′) = 0 where F is a 2π-periodic function in the variable t and ε is a small parameter. Here the prime denotes derivative with respect to the variable t. Different kinds of third-...