I've always gone out of my way to avoid using 'whose' when talking about inanimate objects, for example, 'the book, whose cover is red'. If using 'of which' would be inelegant, I rephrase.
I have just picked up a book which opens with exactly such a construction. A quick Google suggests that it widely considered to be correct and acceptable, and that I am misguided in this particular bit of pedantry (
!). Apparently Fowler endorses it, with the following line from Milton?s Paradise Lost: 'Of man's first disobedience, and the fruit/Of that forbidden tree, whose mortal taste/Brought death into the world [...]'.
What do you all prefer to do?