In calculus (particularly in multivariate calculus, the study of rate of change on functions with multiple variables), the partial derivative of a function is the derivative of one named variable, where all other unnamed variables of the function are held constant. In other words, the partial derivative takes the derivative of certain indicated variables of a function, and does not differentiate the other variable(s).
For the partial derivative of a function "f" with respect to the variable "x", the notations
formula_1, formula_2, formula_3
are usually used, although other notations are valid. Usually, although not always, the partial derivative is taken in a multivariable function (a function which takes two or more variables as input).
If we have a function formula_4, then there are several partial derivatives of "f(x, y)" that are all equally valid. For example,
Or, we can do the following:
String (physics)
In string theory and theoretical physics, strings are hypothetical objects that are believed to be the elementary particles of the universe. If they exist, they would not be point-like particles, but rather 1-dimensional "strings" of energy that vibrate in various dimensions. The image to the right illustrates the various possible dimensions that a string could vibrate in. (Currently, physicists accept the fact that there are at least 11 dimensions in our universe: 1 time dimension and 10 spatial dimensions.) The length of the strings would be determined by Planck length:
It is still not known whether these strings actually exist. They are pretty much the main topic of string theory.
Kathy Ireland
Kathleen Marie "Kathy" Ireland (born March 20, 1963 in Glendale, California) is an American fashion model, actress and businesswoman. She has been featured in "Sports Illustrated" swimsuit issue thirteen times and been on the cover three times. She also acted in several movies and television programs. Her licensing company, Kathy Ireland Worldwide, is responsible for most of her approximately $420 million wealth.
Biff Elliot
Biff Elliot (born Leon Shalek; July 26, 1923 – August 15, 2012) was an American television, stage, voice, radio, and movie actor. He is best known for his role as Mike Hammer in the 1953 movie "I, the Jury", and as his guest appearance in the "Star Trek" episode "The Devil in the Dark".
Elliot was born Leon Shalek on July 26, 1923 in Lynn, Massachusetts to Jack and Susan Elliot, he served in the army and later attended the University of Maine. After he graduated in 1949 he began acting and later appeared in 100 of movies and television programs, his career began and known after his role in "I, the Jury" in 1953.
Elliot was married to Betty Dole from 1948 until her death in 1974. He lastly married Connie Elliot from 1977 until his death in 2012. Elliot died on August 15, 2012 in his Studio City, California home from natural causes, he was 89 years old.
Paul Ryan
Paolo Davis "Paul" Ryan (born January 29, 1970) is an American politician. He was the Speaker of the United States House of Representatives from October 29, 2015 to January 3, 2019. He was a member of U.S. House of Representatives from 1999 to 2019. He was also the House Budget Committee chairman.
Ryan also served as Chairman of the House Budget Committee from 2011 to 2015. He was the Republican Party nominee for Vice President in the 2012 election. On October 22, 2015, Ryan said he was going to run for Speaker of the United States to succeed John Boehner. He was elected on October 29 and shortly afterwards became speaker. As Speaker, Ryan helped launch the House passing of the American Health Care Act.
Ryan announced his retirement from Congress on April 11, 2018.
Ryan was born at Mercyhealth Hospital and Trauma Center in Janesville, Wisconsin. His parents were Elizabeth A. "Judy" (née Hutter) and Paul Murray Ryan. Ryan studied at Miami University in Oxford, Ohio. His father died of a heart attack when Ryan was in his teenage years. His grandmother moved in shortly afterwards because she had Alzheimer's disease.
Ryan was first elected to the House in 1999, winning the 1st District seat of Mark Neumann, a two-term incumbent who had vacated his seat to make an unsuccessful bid for the U.S. Senate. Ryan won the Republican primary over 29-year-old pianist Michael J. Logan of Twin Lakes.
Ryan became the ranking Republican member of the House Budget Committee in 2008, then chairman in 2012 after Republicans took control of the House. That same year he was selected to deliver the Republican response to the State of the Union address.
During his 12 years in the House, Ryan has sponsored more than 70 bills or amendments, of which two were enacted into law. One, passed in July 2000, renamed a post office in Ryan's district; the other, passed in December 2009, lowered the excise tax on arrow shafts. Ryan has also co-sponsored 975 bills, of which 176 have passed. 22 percent of these bills were originally sponsored by Democrats.
In 2010, Ryan was a member of the bipartisan National Commission on Fiscal Responsibility and Reform (Bowles-Simpson Commission), which was tasked with developing a plan to reduce the federal deficit. He voted against the final report of the commission.
In 2012, Ryan accused the nation's top military leaders of using "smoke and mirrors" to remain under budget limits passed by Congress. Ryan later said that he misspoke on the issue and called General Martin Dempsey, the Chairman of the Joint Chiefs of Staff, to apologize for his comments.
As of mid-2012, Ryan had been on seven trips abroad as part of a congressional delegation.
On October 9, 2015, after the resignation of Speaker of the House John Boehner, Ryan confirmed that he might run for speaker. Ryan confirmed on October 22 that he would seek the speakership after receiving the endorsements of two factions of House Republicans, including the conservative Freedom Caucus. On October 29, Ryan was elected Speaker with 236 votes. He is the youngest Speaker since James G. Blaine in 1875. As Speaker, Ryan has had a role in passing the Every Child Suceeds Act, a big school reform law. He has been a major expert on the government budget, and worked with Senator Patty Murray to pass a budget before he was speaker. Ryan was the Speaker of the House during the 2016 Presidential election. On Wednesday, April 11, 2018, Speaker Ryan announced his intent not to re-election saying he will be retiring in January, at the end of his current term.
Ryan announced his retirement from the House on April 11, 2018.
On August 11, 2012, he was selected by Republican Party Presidential Candidate Mitt Romney for Vice Presidential Candidate of the 2012 Presidential election.
Ryan is currently married to Jenna Little. They have three children. Before entering into politics, Ryan worked as a fitness instructor. He was also a speechwriter for New York congressman Jack Kemp during the early 1990s.
Phil Leeds
Phil Leeds (April 6, 1916 – August 16, 1998) was an American television and movie actor. Leeds' eyes, rubbery face and wizened made him known in movies and his guest appearences in television programs such as in; "The Dick Van Dyke Show", "Roseanne", "The Golden Girls", "Three's Comapany", "Friends", "Everybody Loves Raymond", "Wings", "The Patty Duke Show", "The Larry Sanders Show", and as a ghost in the movie "Ghost".
Leeds was born on April 6, 1916 in New York City, New York. Leeds was never married and had no children. Leeds died on August 19, 1998 from pneumonia in Los Angeles, California, he was 82 years old.
Walter Slezak