Question: Who painted the wife of King Philip IV of Spain in 1635?

Context paragraphs:
Elisabeth of France (1602–1644): Elisabeth of France (22 November 1602 – 6 October 1644) was Queen consort of Spain (1621 to 1644) and Portugal (1621 to 1640) as the first spouse of King Philip IV of Spain.  She also served as regent of Spain during the Catalan Revolt.  She was the eldest daughter of King Henry IV of France and his second spouse Marie de' Medici.  As a daughter of the King of France, she was born a "Fille de France".  As the eldest daughter of the king, she was known at court by the traditional honorific of "Madame Royale".

Equestrian Portrait of Elisabeth of France: The portrait Equestrian Portrait of Elisabeth of France was painted by Velázquez of Elisabeth of France "circa" 1635, originally for the Salón de Reinos and now in the Prado since the gallery's institution in 1819.

English expedition to Flanders (1297–98): The English expedition to Flanders (1297–98) was an English expedition to Flanders that lasted from August 1297 until March 1298.  King Edward I of England in an alliance with Guy, Count of Flanders, as part of the wider Anglo-French War (1294–1303), led an English force to Flanders, hoping to form military alliances and support to lead a combined force against King Philip IV of France.  The expedition was a failure in gaining military support and after a peace was reached between King Edward I of England and King Philip IV of France, Edward left Flanders in March 1298.

Treaty of Paris (1657): The Treaty of Paris signed in March 1657 allied the English Protectorate of Oliver Cromwell with King Louis XIV of France against King Philip IV of Spain, merging the Anglo-Spanish War (1654–1660) with the larger Franco-Spanish War (1635-1659).  The treaty confirmed the growing rapprochement between France and the English Republican regime.

Philip IV in Brown and Silver: The Portrait of Philip IV or Philip IV in Brown and Silver is a portrait of Philip IV of Spain painted by Diego Velázquez.  It is sometimes known as "Silver Philip" and is now in the National Gallery in London.  It was the main portrait of Philip painted by Velázquez in the 1630s, used as the model for many workshop versions.

Marquis of Caracena: The title of Marquis of Caracena (Spanish: "Marquesado de Caracena" is a Spanish title of nobility bestowed in 1624 by King Philip IV of Spain on Luis Carrillo de Toledo whom he had elevated from the title of Count of Caracena which King Philip III of Spain had previously granted in 1599.  The 1st Marquis of Caracena was also later created as Count of Pinto.

Equestrian Portrait of Philip IV: The Equestrian Portrait of Philip IV was a portrait of Philip IV of Spain on horseback, painted by Velázquez in 1635-36 as part of a series of equestrian portraits for the Salón de Reinos at the palacio del Buen Retiro in Madrid (a series that also included that of Philip's son prince Balthasar Charles).

Monument to Philip IV of Spain: The Monument to Philip IV or Fountain of Philip IV is a memorial to Philip IV of Spain in the centre of Plaza de Oriente in Madrid, Spain.  It was raised at the insistence of Isabella II of Spain in the first half of the 19th century, opening on 17 November 1843, a year before Narciso Pascual y Colomer came up with the square's final layout.  However, its equestrian statue of the king dates to the 17th century and was produced by the Italian sculptor Pietro Tacca using scientific advice from Galileo Galilei and drawings by Diego Velázquez and a bust by Juan Martínez Montañés (who also collaborated on the work).

Juan de Mendoza, Marquis de la Hinojosa: Juan de Mendoza y Velasco, Marquis de la Hinojosa, Governor of the Duchy of Milan, 1612–1616, Viceroy of Navarre, 1620–1623, Spanish Ambassador in England in 1623 to discuss with the regnant father of the later king Charles I of England the requirements to be, eventually, met by the English politicians to get Prince Charles married to Maria of Austria, sister of the then 19 years old ruling king Philip IV of Spain.  A knight of the Military Order of Santiago, deceased 24 December 1628, was awarded the title of marquis de la Hinojosa by king Philip III of Spain, on 11 February 1612.  Although it is claimed his father was 5th Count of Castrogeriz, it seems under careful inspections that he rather came from a family of landed nobility squires, his father, reported as Antonio Gómez Manrique de Mendoza y Sandoval, being the 6th Sieur of Castrojeriz, and 4th Sieur of Villazopeque, who married first to a certain Isabel de Velasco y nríquez de Ribera, also, apparently, from a rather modest branch of rural proprietors albeit assuming some sort connections with this powerful de Velasco ducal family, (Dukes of Frías).

Philip IV of Spain: Philip IV of Spain (Spanish: "Felipe IV" ; 8 April 1605 – 17 September 1665) was King of Spain (as "Philip IV" in Castille and "Philip III" in Aragon) and Portugal as Philip III (Portuguese: "Filipe III" ).  He ascended the thrones in 1621 and reigned in Spain until his death and in Portugal until 1640.  Philip is remembered for his patronage of the arts, including such artists as Diego Velázquez, and his rule over Spain during the challenging period of the Thirty Years' War.

Supporting paragraphs: Equestrian Portrait of Elisabeth of France Elisabeth of France (1602–1644)
Answer: Velázquez