Q:

How do I differentiate $f(x) = 7 + 6/x + 6/x^2$?

the problem is the following:
with the definition of the derivative, calculate 
f(x) = $7+\frac 6x+ \frac6{x^2}$
I tried to solve it a bunch of times but I just don't get the correct answer
**edit: I must solve it with the def of the derivative

A:

Given $7+\dfrac6x+\dfrac{6}{x^2}$
$$\dfrac{d}{dx}\left(7+\dfrac6x+\dfrac{6}{x^2}\right)$$
$$\dfrac{d}{dx}(7)=0$$
$$\dfrac{d}{dx}\left(\dfrac6x\right)=6\dfrac{d}{dx}(x^{-1})=-6x^{-2}=-\dfrac6{x^2}$$
$$\dfrac{d}{dx}\left(\dfrac{6}{x^2}\right)=6\dfrac{d}{dx}\left(x^{-2}\right)=6(-2)(x^{-3})=-\dfrac{12}{x^3}$$
$$\dfrac{d}{dx}\left(7+\dfrac6x+\dfrac{6}{x^2}\right)=-\dfrac{6}{x^2}-\dfrac{12}{x^3}$$

