How do you differentiate #f(x)=x^3-x^2+4x-1# using the sum rule?

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Answer 1 · 2016-01-18T19:14:03

#f'(x)=3x^2-2x+4#

The Sum Rule says:

#d/dxsum_(i=1)^nk_i*f_i(x)=d/dx[k_1f_1(x)+k_2f_2(x)+...+k_nf_n(x)]=#

#=k_isum_(i=1)^nd/dxf_i(x)=k_1f_1'(x)+k_2f_2'(x)+...+k_nf_n'(x)#

#:.f'(x)=d/dx(x^3)-1*d/dx(x^2)+4d/dx(x)-1d/dx(1)=#

#=3x^(3-1)-1*(2x^(2-1))+4*(1)-1*(0)=#

#=3x^2-2x+4#