Yes, check out Chapter 8 of this paper:
http://www.math.ias.edu/~avi/PUBLICATIONS/MYPAPERS/CKW11/CKW11.pdf
Chapter 8Chen, Xi; Kayal, Neeraj; Wigderson, Avi, Partial derivatives in arithmetic complexity and beyond, Found. Trends Theor. Comput. Sci. 6, No. 1–2, 1–138 (2010). Zbl 1278.68010. PDF
