What is the derivative of #y=1/2(x^2-x^-2)#? Calculus Basic Differentiation Rules Power Rule 1 Answer Yousef A. Feb 5, 2018 #x+x^-3# Explanation: distribute the #1/2#: #x^2/2-x^-2/2# use the power rule: #d/dxx^n=nx^(n-1)# #(2x)/2-(-2x^-3)/2# = #x+x^-3# Answer link Related questions How do you find the derivative of a polynomial? How do you find the derivative of #y =1/sqrt(x)#? How do you find the derivative of #y =4/sqrt(x)#? How do you find the derivative of #y =sqrt(2x)#? How do you find the derivative of #y =sqrt(3x)#? How do you find the derivative of #y =sqrt(x)#? How do you find the derivative of #y =sqrt(x)# using the definition of derivative? How do you find the derivative of #y =sqrt(3x+1)#? How do you find the derivative of #y =sqrt(9-x)#? How do you find the derivative of #y =sqrt(x-1)#? See all questions in Power Rule Impact of this question 1427 views around the world You can reuse this answer Creative Commons License