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

1 Answer
Nov 5, 2017

#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.