How do you differentiate #f(x)=7x^3-x^2+x# using the sum rule? Calculus Basic Differentiation Rules Sum Rule 1 Answer VNVDVI Apr 6, 2018 #f'(x)=21x^2-2x+1# Explanation: #d/dx(7x^3-x^2+x)=d/dx7x^3-d/dxx^2+d/dxx#, we can break up a derivative across sums or differences. Thus, #f'(x)=(3)(7)x^2-2x+1# #f'(x)=21x^2-2x+1# 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 2847 views around the world You can reuse this answer Creative Commons License