It is indeed a continuation from Derby, as the Birmingham Western Suburban Railway (the present day route between Birmingham NS and Kings Norton via University) became part of the Midland Railway.
At the end of the Kings Norton platform at Five Ways, there is a milepost that has 43 1/2 (or 3/4 - I cannot remember exactly). According to the Railmiles website, the distance from Birmingham NS to Five Ways is 74 chains, which is 1 mile if rounded to the nearest quarter mile.
Furthermore, the Railmiles website has Derby to Five Ways as 40 miles 33 chains (40 1/2 miles rounded to the nearest quarter mile), however, this is the shortest route via the London & North Western Railway route via both Lichfield stations.
Breaking it down into two sections via Midland Railway metals, Derby - Water Orton is 33miles and 59 Chains (33 3/4 miles), with Water Orton - Five Ways being 8 miles and 47 chains (8 1/2 miles), giving a total of 42 1/4 miles. This is via the cut off route between Water Orton and Wilnecote.
Derby - Whitacre Junction is 32 miles and 3 chains (32 miles), and Whitacre Junction to Five Ways is 11 miles 32 chains (11 1/2 miles), giving a total of 43 1/2 miles Derby - Five Ways via Whitacre Junction.
Hope the above helps.