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  2. Second derivative - Wikipedia

    en.wikipedia.org/wiki/Second_derivative

    The second derivative of a function f can be used to determine the concavity of the graph of f. [2] A function whose second derivative is positive is said to be concave up (also referred to as convex), meaning that the tangent line near the point where it touches the function will lie below the graph of the function.

  3. 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 () = (), where both f and g are differentiable and () The quotient rule states that the derivative of h(x) is

  4. Differentiation rules - Wikipedia

    en.wikipedia.org/wiki/Differentiation_rules

    For any functions and and any real numbers and , the derivative of the function () = + with respect to is ′ = ′ + ′ (). In Leibniz's notation , this formula is written as: d ( a f + b g ) d x = a d f d x + b d g d x . {\displaystyle {\frac {d(af+bg)}{dx}}=a{\frac {df}{dx}}+b{\frac {dg}{dx}}.}

  5. Product rule - Wikipedia

    en.wikipedia.org/wiki/Product_rule

    In calculus, the product rule (or Leibniz rule [1] or Leibniz product rule) is a formula used to find the derivatives of products of two or more functions.For two functions, it may be stated in Lagrange's notation as () ′ = ′ + ′ or in Leibniz's notation as () = +.

  6. General Leibniz rule - Wikipedia

    en.wikipedia.org/wiki/General_Leibniz_rule

    The proof of the general Leibniz rule [2]: 68–69 proceeds by induction. Let and be -times differentiable functions.The base case when = claims that: ′ = ′ + ′, which is the usual product rule and is known to be true.

  7. Numerical differentiation - Wikipedia

    en.wikipedia.org/wiki/Numerical_differentiation

    Differential quadrature is the approximation of derivatives by using weighted sums of function values. [22] [23] Differential quadrature is of practical interest because its allows one to compute derivatives from noisy data.

  8. Derivative - Wikipedia

    en.wikipedia.org/wiki/Derivative

    Suppose that a function represents the position of an object at the time. The first derivative of that function is the velocity of an object with respect to time, the second derivative of the function is the acceleration of an object with respect to time, [28] and the third derivative is the jerk. [35]

  9. Vector calculus identities - Wikipedia

    en.wikipedia.org/wiki/Vector_calculus_identities

    2 First derivative identities. ... where i, j, k are the standard unit vectors for the x, y, z-axes. More generally, for a function of n variables ...