How do you find the derivative of #f(x)=1/x^5#? Calculus Basic Differentiation Rules Power Rule 1 Answer Henry W. Oct 22, 2016 #f'(x)=-5/x^6# Explanation: #1/x^5# is the same as #x^-5# #:.f(x)=x^-5# #f'(x)=-5x^-6=-5/x^6# Or, using quotient rule, Let #u=1, v=x^5# #f'(x)=((0)x^5-(1)5x^4)/x^10# #=(-5x^4)/x^10=-5/x^6# 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 3165 views around the world You can reuse this answer Creative Commons License