What is the derivative of x+1/x according to the definition?

Question

Its been forever since I've used the x+h method and I am absolutely lost as to where to begin. I know its supposed to be 1-1/x^2 but I'm drawing a complete blank. Help please!

Answer 1

Fundamental theorem of differentiation: 

Rewrite the expression with common denominator.

Rewrite the expression with common denominator.

= 

Therefore the derivative of is  .