Question

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

Answer 1

`f'(x) = -1/x^2 + 1`

Explanation:

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

`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 `-1/x^2`. So, the derivative of the first term is `-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'(x) = -1/x^2 + 1`. I hope this helped.