Second derivative

In calculus, the second derivative, or the second order derivative, of a function f is the derivative of the derivative of f. Roughly speaking, the second derivative measures how the rate of change of a quantity is itself changing; for example, the second derivative of the position of a vehicle with respect to time is the instantaneous acceleration of the vehicle, or the rate at which the velocity of the vehicle is changing with respect to time. In Leibniz notation:

On the graph of a function, the second derivative corresponds to the curvature or concavity of the graph. The graph of a function with positive second derivative curves upwards, while the graph of a function with negative second derivative curves downwards.

Second derivative power rule

The power rule for the first derivative, if applied twice, will produce the second derivative power rule as follows:

Notation

The second derivative of a function is usually denoted . That is:

When using Leibniz's notation for derivatives, the second derivative of a dependent variable y with respect to an independent variable x is written

Derivative

The derivative of a function of a real variable measures the sensitivity to change of a quantity (a function value or dependent variable) which is determined by another quantity (the independent variable). Derivatives are a fundamental tool of calculus. For example, the derivative of the position of a moving object with respect to time is the object's velocity: this measures how quickly the position of the object changes when time is advanced.

The derivative of a function of a single variable at a chosen input value, when it exists, is the slope of the tangent line to the graph of the function at that point. The tangent line is the best linear approximation of the function near that input value. For this reason, the derivative is often described as the "instantaneous rate of change", the ratio of the instantaneous change in the dependent variable to that of the independent variable.

Derivatives may be generalized to functions of several real variables. In this generalization, the derivative is reinterpreted as a linear transformation whose graph is (after an appropriate translation) the best linear approximation to the graph of the original function. The Jacobian matrix is the matrix that represents this linear transformation with respect to the basis given by the choice of independent and dependent variables. It can be calculated in terms of the partial derivatives with respect to the independent variables. For a real-valued function of several variables, the Jacobian matrix reduces to the gradient vector.

FX

FX, F-X, F/X, Fx, or fx may refer to:

Arts, media, and entertainment

(See also below: Arts, media, and entertainment technology)

Film and television

Music

Print

Medicine

Technology

X (manga)

X (Japanese: エックス, Hepburn: Ekkusu), also known as X/1999, is a Japanese shōjo manga series created by Clamp, a creative team made up by Satsuki Igarashi, Nanase Ohkawa, Tsubaki Nekoi, and Mokona. It premiered in Monthly Asuka's May 1992 issue and ran there until the magazine's editors showed concern in the increasingly violent stories. The series went on long-term hiatus in March 2003 and has yet to be concluded. The story takes place at the end of days, in the year 1999. The series follows Kamui Shirō, a young esper who returns home to Tokyo after a 6-year absence to face his destiny as the one who will determine humanity's fate.

Kadokawa Shoten collected and published the individual chapters in 18 tankōbon volumes, with five chapters published in the book "All about Clamp". All but several final chapters have been published. It has been adapted into a series of audio dramas, a 1996 animated feature film and a television series in 2001 with the two latter produced by Madhouse. Viz Media published all 18 volumes in North America, while the film and the TV series have released in DVDs by Manga Entertainment and Geneon, respectively.

F/X: The Series

F/X: The Series is a television series based on the film F/X, starring Cameron Daddo, Christina Cox, Kevin Dobson (season 1), Jacqueline Torres (season 2), Carrie-Anne Moss and Jason Blicker. It ran for 40 episodes from 1996 through 1998.

Much or all of the show was filmed in Toronto, Ontario, Canada (save for stock footage to make it appear to be New York City). The opening sequence ended with a television crew in the foreground loading trucks, and an enormous advertisement (painted on the rear of a building) for The Phantom of the Opera, of which a theatrical production was showing in Toronto at the time.

Premise

The show focuses on Rollie Tyler (Cameron Daddo), a special effects man in NYC, who assists NYPD detective Leo McCarthy (Kevin Dobson) in capturing criminals. In the second season, Dobson's character was killed and replaced with Mira Sanchez (Jacqueline Torres).

DVD releases

Alliance Home Entertainment has released the entire series on DVD in Region 1 (Canada only).