How do you differentiate #f(x)=3/x-5/(1-x)# using the sum rule? Calculus Basic Differentiation Rules Sum Rule 1 Answer Kalyanam S. Jun 2, 2018 #color(maroon)(f’(x) = -(3/x^2 + 5/(1-x)^2)# Explanation: #f(x) = (3/x) - (5/(1-x))# #f(x) = 3x^-1 - 5(1-x)^-1# #f’(x) = (3 * -1* x^-2) - (5 * -1 (1-x)^-2 * -1)# #f’(x) = -3x^-2 - 5(1-x)^-2# #color(maroon)(f’(x) = -(3/x^2 + 5/(1-x)^2)# Answer link Related questions What is the Sum Rule for derivatives? How do you find the derivative of #y=f(x)+g(x)#? How do you find the derivative of #y = f(x) - g(x)#? What is the derivative of #f(x) = xlnx-lnx^x#? How do you differentiate #f(x)=1/x+1/x^3# using the sum rule? How do you differentiate #f(x)=x+x-2x# using the sum rule? How do you differentiate #f(x)=x^2-x-x(x-1)# using the sum rule? How do you differentiate #f(x)=x^3-x^2+4x-1# using the sum rule? How do you differentiate #f(x)=sinx+cosx-x^3# using the sum rule? How do you differentiate #f(x)=x+lnx^2-x^2# using the sum rule? See all questions in Sum Rule Impact of this question 2031 views around the world You can reuse this answer Creative Commons License