Question

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

Answer 1

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

Explanation:

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`