Find the first and second derivative of f(x) = 6/x^2 + 2x

We can rewrite the function to eliminate the annoying 1/x^2 expression by knowing this can also be expressed by x^-2.f(x) = 6x^-2 + 2xNow we can differentiate this function term by term, first 6x^-2. We know the rule for differentiating a term is kx^(k-1).In this case k = -2, so this gives us -12x^-3.Now for the next term k = 1, so we get 2.Putting them together we get:f'(x) = -12x^-3 + 2 or to reintroduce the fraction, -12/x^3 + 2.
To get the second derivative we do the same thing with our newly found first derivative, we takef'(x) = -12x^-3 + 2 and differentiate this term by term. For the term -12x^-3, k = -3, so we get 36x^-4. For our second term k = 0, and so we get 0. So our final second derivative is:f''(x) = 36x^-4 or 36/x^4