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2. Quotient rule - Wikipedia

   en.wikipedia.org/wiki/Quotient_rule

   In calculus, the quotient rule is a method of finding the derivative of a function that is the ratio of two differentiable functions. Let () = () ...

3. Integration by parts - Wikipedia

   en.wikipedia.org/wiki/Integration_by_parts

   The rule is sometimes written as "DETAIL", where D stands for dv and the top of the list is the function chosen to be dv. An alternative to this rule is the ILATE rule, where inverse trigonometric functions come before logarithmic functions. To demonstrate the LIATE rule, consider the integral ⁡ ().

4. Fractional calculus - Wikipedia

   en.wikipedia.org/wiki/Fractional_calculus

   The corresponding derivative is calculated using Lagrange's rule for differential operators. To find the α th order derivative, the n th order derivative of the integral of order (n − α) is computed, where n is the smallest integer greater than α (that is, n = ⌈α⌉). The Riemann–Liouville fractional derivative and integral has ...

5. Synthetic division - Wikipedia

   en.wikipedia.org/wiki/Synthetic_division

   Animation showing the use of synthetic division to find the quotient of + + + by .Note that there is no term in , so the fourth column from the right contains a zero.. In algebra, synthetic division is a method for manually performing Euclidean division of polynomials, with less writing and fewer calculations than long division.

6. Jacobian matrix and determinant - Wikipedia

   en.wikipedia.org/wiki/Jacobian_matrix_and...

   Composable differentiable functions f : R n → R m and g : R m → R k satisfy the chain rule, namely () = (()) for x in R n. The Jacobian of the gradient of a scalar function of several variables has a special name: the Hessian matrix , which in a sense is the " second derivative " of the function in question.

7. Symbolab - Wikipedia

   en.wikipedia.org/wiki/Symbolab

   Symbolab is an answer engine [1] that provides step-by-step solutions to mathematical problems in a range of subjects. [2] It was originally developed by Israeli start-up company EqsQuest Ltd., under whom it was released for public use in 2011. In 2020, the company was acquired by American educational technology website Course Hero. [3] [4]

8. Finite difference - Wikipedia

   en.wikipedia.org/wiki/Finite_difference

   In an analogous way, one can obtain finite difference approximations to higher order derivatives and differential operators. For example, by using the above central difference formula for f ′(x + ⁠ h / 2 ⁠) and f ′(x − ⁠ h / 2 ⁠) and applying a central difference formula for the derivative of f ′ at x, we obtain the central difference approximation of the second derivative of f:

9. Vector calculus identities - Wikipedia

   en.wikipedia.org/wiki/Vector_calculus_identities

   The validity of this rule follows from the validity of the Feynman method, for one may always substitute a subscripted del and then immediately drop the subscript under the condition of the rule. For example, from the identity A ⋅( B × C ) = ( A × B )⋅ C we may derive A ⋅(∇× C ) = ( A ×∇)⋅ C but not ∇⋅( B × C ) = (∇× B ...