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

Answered by Maths tutor

2996 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Differentiate "sin(2x)"


Find X log(x)=4 Base 10


The line AB has equation 5x + 3y + 3 = 0 and it intersects the line with equation 3x - 2y + 17 = 0 at the point B. Find the coordinates of B.


How do I find the stationary points on the curve y = f(x) = x^3+6x^2-36x?


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning