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It is noted that discretized model (3.1) can be considered as using the standard Euler method for the first derivative and a nonlocal expression for nonlinear terms.
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The square integral estimate for the first derivative of convex function was established in [1, 2].
where f ̇ and h ̇ stand for the first derivatives of the functions f and h, respectively.
The second and third criterions are for the first derivatives of the functions.
In that way one can find integral representations for the first derivatives of the solution which do not involve the first derivatives of function H.
For (beta ) non-zero, the first derivative of Eq. (7) must be zero and the second derivative positive.
For variable V, the magnitude, the first and second derivatives are used; for variable q o and q i, only the magnitude and the first derivative are used.
Compare first derivative, and second derivative : : First derivative – the derivative of a function, example: "Velocity is the first derivative of distance with respect to time".
For the no-error estimation of distance the first derivative is equal to interhydrophone distance.
When using this notation for the second derivative, you must write: d2y/dx2.
In Equation 34, the calculation of the first derivative are re-used for calculating the second derivative thus reducing the computational load.
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