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
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, 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
- F/X: The Series, a television program based on the movie
Music
Medicine
Technology
Podcasts:
F-X
ALBUMS
- Every One a Classic, Volume 6 released: 2001
- England Belongs to Me, Volume 1 released: 1998
- Killed by Death #100 released: 1996
- Souths Gonna Rise Again released: 1979
f(x)
FX
ALBUMS
- Sunshine Live, Volume 19 released: 2006
- Dance House, Volume 1 released:
- Only for DJ's: Techno Traxx , Volume 8 released:
- Club Sounds: The Ultimate Club Dance Collection, Volume 38 released:
Dance House, Volume 1
- Rockin'
- Tell Me Why
- Cuba (2-4 Grooves radio edit)
- Gotta Let You Go
- Once in a Lifetime Groove
- My Arms Keep Missing You
- Feel Alive (original extended)
- Forever
- Don't You Want Me
- Ring of Fire (Stadium edit)
- Cold Days (2-4 Grooves radio edit)
- Just the Way It Is (Scotty short remix)
- Living on Video (Alex M. remix edit)
- One Night
- Let's Get Down (Full Intention radio mix)
- Rock With You
- What's Up
- I Can't Sleep!
- Miles of Love
- Esta Loca (Alex M. radio edit)
Only for DJ's: Techno Traxx , Volume 8
- Ha Deng (Pulsedriver remix)
- Bad and Sexy (Pulsar Crew remix)
- The Ground (DJ Merlyn remix)
- Stupid Games (club mix)
- Fly Guy (DJ Pain remix)
- Set You Free (Dave-X remix)
- Fantsy (Fantasy Trance mix)
- Urban Train (Marc O' Tool instrumental mix)
- Love Freedom Tolerance (Rave mix)
- Storm (Geert Huinink 2001 remix)
- Right Here, Right Now (X-tended mix)
Club Sounds: The Ultimate Club Dance Collection, Volume 38
- World, Hold On (Axwell remix edit) (feat. Steve Edwards)
- Bakerman (Funktune radio edit)
- My Arms Keep Missing You (radio edit)
- Cold Days (original radio mix)
- Cuba (Sunset Crew radio)
- Gotta Let U Go (short mix)
- Big Fun (radio edit)
- Ghost Town (feat. Johnny Logan) (edit)
- You Got the Love (feat. Candi Staton) (Shapeshifters radio edit)
- That Once in a Lifetime (Hi_tack edit)
- Keep on Tryin' (feat. Emily Chick) (Raw Shape remix)
- Mymymy 2006 (feat. Tara McDonald) (Stonebridge remix)
- Me & U (Spencer & Hill radio edit)
- Better World (original mix)
- Be My Friend (feat. D'Empress) (Michael Gray radio mix)
- I Like It (feat. Anthony Locks) (original)
- Candy (original edit)
- Rockin (radio mix)
- Prime Time of Your Life (Para One remix)
- One More Night (original radio cut)
- Easy (feat. Valeska) (original radio edit)
F[]X(Resistance Unit)
ALBUMS
- Free Electrons, Volume 2 released: 2009
- Free Electrons, Volume 1 released: 2008
Free Electrons, Volume 2
Released 2009- Fear of the Unknown
- Mystical Silence
- Starfall
- Psych-O-Matic
- Stupid
- Night City
- The Side
- Second Sight
- Silent Force (instrumental)
- Spiral Inside
- Faces of Night
- Croatia (vocal version)
- Annie, Yo!
- Hall of Evil (feat. Almaz)
- Scopeville
- To Fix the Time
- Irreversible, Part 3
- Love of My Life (original mix)
- Piel
- Wrong Hookah
F/X
ALBUMS
- Technics DJ Set, Volume Three released: 2001
Technics DJ Set, Volume Three
Released 2001- Dreams (Cosmic Gate remix)
- The Legacy (club mix)
- Airwave (club mix)
- Follow Me (Mas mix)
- Spirit of Space (The Temple Theatre mix)
- Trauma (DuMonde dub mix)
- At the End (original mix)
- First Impression (S.H.O.K.K. mix)
- Paranoid (DJ Scot Project remix)
- Klinisch Tot (club UK mix)
- Joyenergizer (Phisical 1 mix)
- Maschine Eisenbass (original mix)
- Kyoto Protocol (original mix)
- Manipulated (Adam Beyer mix)
- Remis Playaz (Alter Ego remix)
- Absolut (club mix)
- Like This Like That (Oliver Klein remix)
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Signal
by: F(x)Turn on my radio, stay tuned
I’ve got a Signal eoje kkume nareul
Chajaon huimi hadeon jageun shinho
Eojjeomyeon meolli alji motaneun nugunga
Naege gujoreul yocheong Whoa
Jogeumeun uurhaetdeon yojeumui
Nae pyojeongeul neon gamanhi manjigon
Dashi jogeumsshig meoreojyeo ga
Machi utneun deushi
Dashi kyeo boja Radio
Ne shigeu neoreul jabeul su itge
(Mono animyeon Stereo)
Tto dashi mureumpyo neol jabeun
Dwien eotteohge kib hal su itni?
Woo- tumyeonghan geu mome
Geumul deonjyeo bolkka
Woo- neoreul nohchin dwien
Eotteohge gyeondil su itni?
Saenggage ppajyeo mot he eona
From 9 to 5, 5 to 9 michyeoga
Eojjeomyeon dashi gwedoreul dora
Nareul seollege jam mot deulge hae Whoa
Sentimenteol romaenseu geureon geon
Gwanshim eobtneun nae sshig sshig han harue
Jageun dol deonjyeo beorigon ga
Machi utneun deushi
Dashi kyeo boja Radio
Ne shigeu neoreul jabeul su itge
(Mono animyeon Stereo)
Tto dashi mureumpyo neol jabeun
Dwien eotteohge kib hal su itni?
Woo- tumyeonghan geu mome
Geumul deonjyeo bolkka
Woo- neoreul nohchin dwien
Eotteohge gyeondil su itni?
I’ll be an astronaut,
I’m searching on into space
Turn on my radio, can you hear me?
Jabhiji anhneunde boijido anhneunde
Eodum sog heoujeog daedo
Neon eodi itneun geoya?
Dashi kyeo boja Radio
Ne shigeu neoreul jabeul su itge
(Mono animyeon Stereo)
Tto dashi mureumpyo neol jabeun
Dwien eotteohge kib hal su itni?
Woo- tumyeonghan geu mome
Geumul deonjyeo bolkka
Woo- neoreul nohchin dwien
Eotteohge gyeondil su itni?