Hadiths About the Recommendation to Fast theFirst 10 Days of Dhul-Hijjah
Question

 from the article on your website, entitled The First Ten Days of Dhul-Hijjah, I understood that it is mustahabb (recommended) to fast on the ninth day, but you did not say whether it is Sunnah to also fast on the other days of the ten. There are hadiths, of which I do not know the soundness, which speak of the virtue of these days and encourage doing a lot of deeds of obedience during them, including fasting.
These hadiths are as follows:

1-It was narrated from Abu Hurayrah (may Allah be pleased with him) that the Prophet (blessings and peace of Allah be upon him) said: “There are no days in this world in which worship is more beloved to Allah than the first ten days of Dhul-Hijjah. Fasting on one of these days is equivalent to fasting for a year, and one night of them is equal to Laylat al-Qadar.” (Narrated by At-Tirmidhi, Ibn Majah and al-Bayhaqi)
2-It was narrated that Hafsah (may Allah be pleased with her) said: There are five things that the Prophet (blessings and peace of Allah be upon him) never failed to do: fasting the day of ‘Ashura’, (fasting) the first ten days of Dhul-Hijjah, (fasting) three days of every (Hijri) month, praying two rak`ahs (units of prayer) before Fajr… (Narrated by Ahmad and An-Nasa’i)
From these hadiths, I understand that it is Sunnah to fast on the ninth day and indeed on the rest of the first ten days. Is this correct? Why is that not mentioned in the article? Are the hadiths I mentioned sahih (authentic)?
Praise be to Allah.Firstly: 
On our website we have previously stated that it is mustahabb (recommended) to fast the first nine days of Dhul-Hijjah. Please see the answers to questions no.41633 , 49042  and 84271  
Secondly: 
Degree of the Hadith (Fasting on one of these days (the first ten days of Dhul-Hijjah) is equivalent to fasting for a year)
With regard to the hadith narrated from Abu Hurayrah, according to which the Prophet (blessings and peace of Allah be upon him) said: “There are no days in this world in which worship is more beloved to Allah than the first ten days of Dhul-Hijjah. Fasting on one of these days is equivalent to fasting for a year, and one night of them is equal to Laylat al-Qadar.”
Narrated by At-Tirmidhi (no. 758); al-Bazzar (no. 7816) and Ibn Majah (1728) via Abu Bakr ibn Nafi‘ al-Basri, who said: Mas‘ud ibn Wasil told us, from Nahhas ibn Qaham, from Qatadah, from Sa‘id ibn al-Musayyab, from Abu Hurayrah. 
This is a da‘if isnad (weak chain of transmission) because of an-Nahhas ibn Qaham and Mas‘ud ibn Wasil. Hence the scholars of hadith unanimously agreed that it is to be classed as da‘if (weak). 
At-Tirmidhi (may Allah have mercy on him) said: 
“This is a gharib hadith, which we know only from the hadith of Mas‘ud ibn Wasil, from an-Nahhas. 
I asked Muhammad – i.e., al-Bukhari – about this hadith and he did not know it except via this isnad. 
Some of this was also narrated from Qatadah, from Sa‘id ibn al-Musayyab, from the Prophet (blessings and peace of Allah be upon him) in a mursal report. Yahya ibn Sa‘id criticised An-Nahhas ibn Qaham with regard to his memory.”
Al-Baghawi (may Allah have mercy on him) said: 
“Its isnad is da‘eef.” (Sharh as-Sunnah, 2/624) 
Shaykh al-Islam Ibn Taymiyyah (may Allah have mercy on him) said:
“There is some weakness in it.” (Sharh al-‘Umdah, 2/555) 
Al-Hafizh Ibn Hajar (may Allah have mercy on him) said: 
“Its isnad is da‘if.” (Fath al-Bari, 2/534) 
It was classed as da‘if by Shaykh al-Albani (may Allah have mercy on him) in as-Silsilah ad-Da‘ifah (no. 5142). 
Al-Hafizh Ibn Rajab (may Allah have mercy on him) said – after quoting this and other hadiths on this topic –: 
“Concerning the multiplication of the reward, there are other marfu‘ hadiths, but they are fabricated. Therefore, we turn away from them and similar fabricated reports about the virtues of the first ten days [of Dhul-Hijjah], of which there are many.” (Lata’if al-Ma‘arif, p. 262) 
Thirdly: 
Degree of the hadith (There are five things that the Prophet (peace and blessings of Allah be upon him) never failed to do…)
With regard to the second hadith mentioned in the question – There are five things that the Prophet (blessings and peace of Allah be upon him) never failed to do… – it is based on the report narrated by Hunaydah ibn Khalid al-Khuza‘i, from whom it was narrated via many isnads, in several versions. 
The first isnad is:
Hunaydah ibn Khalid, from the Mother of the Believers Hafsah (may Allah be pleased with her). 
It was narrated from him by al-Hurr ibn as-Sayyah, and this version was narrated from al-Hurr by three narrators: 
1.       ‘Amr ibn Qays al-Mala’i
This was narrated by an-Nasa’i in as-Sunan (2416), Ahmad in al-Musnad (44/59), at-Tabarani in al-Mu‘jam al-Kabeer (23/205), Ibn Hibban in his Sahih (14/332), and Abu Ya‘la in al-Musnad (12/469) as follows: “There are four things that the Prophet (blessings and peace of Allah be upon him) never failed to do: fasting ‘Ashura’, (fasting the first) ten (days of Dhul-Hijjah), fasting three days of every (Hijri) month, and praying two rak‘ahs before Fajr.” The one who narrated it from ‘Amr ibn Qays is Abu Ishaq al-Ashja‘i, who is majhul (unknown), hence it was classed as da‘if by the commentators on al-Musnad and by Shaykh al-Albani in Irwa’ al-Ghaleel (4/111). 
2.                   Zuhayr ibn Mu‘awiyah Abu Khaythamah
This was narrated by an-Nasa’i in al-Kubra (2/135). The version of Zuhayr is as follows: The Messenger of Allah (blessings and peace of Allah be upon him) used to fast three days of every (Hijri) month, the first Monday of the month, then (the first) Thursday, then the Thursday after that. 
3.                   Shurayk
This was narrated by an-Nasa’i in al-Kubra (2/135), and Ahmad in al-Musnad (9/460 – Mu’sasat ar-Risalah ed.). Shurayk narrated it from Ibn ‘Umar with the wording of Zuhayr. 
Ibn Abi Hatim (may Allah have mercy on him) said: 
“I asked my father and Abu Zar‘ah about the hadith: It was narrated by Shurayk, from al-Hurr ibn as-Sayyah, from Ibn ‘Umar, that the Prophet (blessings and peace of Allah be upon him) used to fast of each (Hijri) month the (first) Monday, the Thursday that followed it, then the Monday that followed that. 
They said: This is wrong; rather it is al-Hurr ibn Sayyah, from Hunaydah ibn Khalid, from his wife, from Umm Salamah, from the Prophet (blessings and peace of Allah be upon him).” (Al-‘Ilal, 1/231) 
The commentators on al-Musnad said: 
“Its isnad is da‘if. Shurayk – who is ibn ‘Abdullah an-Nakha‘i – had a poor memory.” (Al-Musnad (9/460) 
The second isnad is:
From Hunaydah ibn Khalid, from his wife, from one of the wives of the Prophet (blessings and peace of Allah be upon him). 
This was narrated by Abu ‘Awanah, from al-Hurr ibn as-Sayyah, from Hunaydah. With this isnad it was narrated by Abu Dawud (no. 2437), an-Nasa’i (2372 and 2418), Ahmad (37/24 and 44/69), al-Bayhaqi in as-Sunan al-Kubra (4/284), and at-Tahawi in  Sharh Ma‘ani al-Athar (2/76). Its wording in the report narrated by Abu Dawud is:
The Messenger of Allah (blessings and peace of Allah be upon him) used to fast nine days of Dhul-Hijjah, the day of ‘Ashura’, and three days of every (Hijri) month: the first Monday of the month and the (following) Thursday. 
The third isnad is:
From Hunaydah, from his mother, from Umm Salamah Via Muhammad ibn Fudayl, who said: al-Hasan ibn ‘Ubaydullah told us: from Hunaydah al-Khuza‘i, from his mother, from Umm Salamah who said: The Messenger of Allah (blessings and peace of Allah be upon him) used to enjoin us to fast three days: the first Thursday, and Monday. According to one report, the Messenger of Allah (blessings and peace of Allah be upon him) used to instruct me to fast three days of every (Hijri) month: Monday, Thursday and the Monday of the following week. According to yet another report: the Messenger of Allah (blessings and peace of Allah be upon him) used to instruct me to fast three days of every (Hijri) month, the first of which was Monday, and Friday, and Thursday.
Narrated by Ahmad (44/82); Abu Ya‘la in al-Musnad (12/315); Abu Dawud (2452); an-Nasa’i (4/221). There is no mention in this report of fasting the first nine days of Dhul-Hijjah or the day of ‘Ashura’; rather it speaks only of fasting three days of every (Hijri) month. 
The fourth isnad:
From Hunaydah, from his wife, from Umm Salamah, 
Via ‘Abd ar-Rahim ibn Sulayman, from al-Hasan ibn ‘Ubaydullah, from al-Hurr ibn Sayyah, from Hunaydah ibn Khalid, from his wife, from Umm Salamah – with the wording mentioned above. This was narrated by at-Tabarani in al-Mu‘jam al-Kabir (23/216 and 23/420), and by Abu Ya‘la in al-Musnad. 
The fifth isnad:
From Hunaydah ibn Khalid who said: I entered upon the Mother of the Believers – and he did not mention her name – 
Via Zuhayr ibn Mu‘awiyah, from al-Hurr ibn as-Sayyah. He said: I heard Hunaydah al-Khuza‘i say: I entered upon the Mother of the Believers and heard her say: The Messenger of Allah (blessings and peace of Allah be upon him) used to fast three days of every (Hijri) month, the first Monday of the month, then the Thursday, then the following Thursday. (Narrated by an-Nasa’I, no. 2415)
To conclude, the critics of hadith differed as to the classification of this hadith because each of these versions has its own isnad and text. 
The hadith was classed as da‘if by az-Zayla‘i in Nasb ar-Rayah (2/157); the commentators on Musnad Ahmad; Shaykh Ibn Baz in Majmu‘ Fatawa Ibn Baz (15/417) – because of the variations in its isnad and text. Perhaps this is the soundest ruling concerning the verdict on this hadith. 
In Sahih Abi Dawud (7/196-199), Shaykh al-Albani classed as sahih the two reports of Zuhayr ibn Mu‘awiyah and Abu ‘Awanah from al-Hurr ibn as-Sayyah. 
It says in Al-‘Ilal by ad-Daraqutni (15/121-122): 
“Hunaydah ibn Khalid al-Khuza‘i was asked about the hadith from Hafsah, who said: There are four things that the Prophet (blessings and peace of Allah be upon him) never failed to do: fasting the day of ‘Ashura’, (fasting) the first ten days of Dhul-Hijjah, (fasting)three days of every (Hijri) month, and praying two rak‘ahs before Fajr. 
He said:
It was narrated by al-Hurr ibn as-Sayyah, from Hunaydah ibn Khalid al-Khuza‘i, from Hafsah. 
Al-Hasan ibn ‘Ubaydullah narrated it via a different isnad: It was narrated by ‘Abd ar-Rahman ibn Sulayman, from al-Hasan ibn ‘Ubaydullah, from his mother, from Umm Salamah. It was also narrated by Abu ‘Awanah, from al-Hurr ibn as-Sayyah, from Hunaydah, from his wife, from one of the wives of the Prophet (blessings and peace of Allah be upon him), but he did not mention her name.” 
And Allah knows best