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?