Helping Ada Lovelace with her Homework: Classroom Exercises from a Victorian Calculus Course – Problem 4

Moving now to calculus, one of the first books De Morgan recommended that Lovelace should study was George Peacock’s Collection of Examples of the Application of the Differential and Integral Calculus, which contained a host of problems and their solutions for students to practice. One of the first problems in the book was to find the differential (not the derivative) of \(u=x^2(a+x)^3(b-x)^4\) [Peacock 1820, 2]. When attempting this question, Lovelace obtained
\[du=\{2ab-(6a-5b)x-x^2 \}x(a+x)^2(b-x)^3 dx\]
whereas the book gave
\[du=\{2ab-(6a-5b)x-9x^2 \}x(a+x)^2(b-x)^3 dx\]
`& I am inclined to think it is a misprint in the latter’ [LB 170, 10 Nov. [1840], f. 63r].

Figure 9. George Peacock (1791–1858), frontispiece of Alexander Macfarlane’s
1916 Lectures on Ten British Mathematicians of the Nineteenth Century.

So who was correct, Lovelace or Peacock?

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