How do you differentiate #f(x)=sinx-1/(xcosx)# using the sum rule? Calculus Basic Differentiation Rules Sum Rule 1 Answer VinÃcius Ferraz Jun 7, 2017 #D_x f(x) = cos x + (cos x + x sin x)/(x^2 cos^2 x)# Explanation: #D_x f = cos x - D_x 1/u# where #u = x cos x# #D_x f = cos x + 1/u^2 D_x (x cos x)# #D_x f = cos x + 1/u^2 (1 cos x + x sin x)# 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 2153 views around the world You can reuse this answer Creative Commons License