# How do you differentiate f(x)=1/x+x using the sum rule?

Nov 5, 2017

$f ' \left(x\right) = - \frac{1}{x} ^ 2 + 1$

#### Explanation:

The Sum Rule simply states that you take the derivative of each term and add them together.

$\frac{1}{x}$ can be re-written as ${x}^{-} 1$. This makes it clear that you want to use the Power Rule with this one. So, using the Power Rule, you bring down the $- 1$ from the exponent, and the exponent decreases to $- 2$. $- {x}^{-} 2$ is written as $- \frac{1}{x} ^ 2$. So, the derivative of the first term is $- \frac{1}{x} ^ 2$.

The second term is easy - you should know that the derivative of x is 1. If you don't, you can apply the Power Rule again, and receive an answer of ${x}^{0}$, which is $1$.

So, when you use the Sum Rule, you add these derivatives together. The result is: $f ' \left(x\right) = - \frac{1}{x} ^ 2 + 1$. I hope this helped.