What is the derivative of #x!#? Calculus Power Series Differentiating and Integrating Power Series 1 Answer Wataru Dec 12, 2014 #x!# is defined only for #x=0,1,2,...#, so the derivative of #x!# does not exist. I hope that this was helpful. Answer link Related questions How do you find the derivative of a power series? How do you find the #n#-th derivative of a power series? How do you use differentiation to find a power series representation for #1/(6+x)^2#? How do you use differentiation to find a power series representation for #f(x)=1/(1+x)^2#? See all questions in Differentiating and Integrating Power Series Impact of this question 1869 views around the world You can reuse this answer Creative Commons License