If `f(x)=|x+a^2a b a c a b x+b^2b c a bb c x+c^2|,fin df^(prime)(x)dot`

Explanation

`f(x) = [(x+a^2)(x+b^2)(x+c^2) + 2a^2b^2c^2] - [a^2bc(x+b^2) + b^2c^2(x+a^2) + a^2b^2(x^2 + x^2)]`

`f(x) = (x^2 + x(a^2 + b^2) +a^2b^2)(x+ c^2) + 2a^2b^2c^2 - a^2bcx - a^2b^3c - b^2c^2x- a^2b^2c^2 - a^2b^2x - a^2b^2c^2`

`f(x) = x^3 + x^2(a^2 + b^2 + c^2) + x(a^2b^2 + c^2a^2 + b^2c^2) + a^2b^2c^2 - a^2bcx - a^2b^3c - b^2c^2x - a^2b^2x`

`f'(x) = 3x^2 + 2x(a^2 + b^2 + c^2) + (a^2b^2 + b^2 c^2 +c^2a^2) -a^2bc - b^2c^2 - a^2b^2 `

`f'(x) = 3x^2 + 2x (a^2 + b^2 + c^2) + a^2(c^2 - bc) `

Answer