Find the derivative of m(x)=1/(x+1) by using the definition of the derivative.

Answer 1

we want the limit as h->0 of

[m(x+h)-m(x)]/h
= [1/(x+1+h) - 1/(x+1)]/h
= [(x+1) - (x+1+h)] / h(x+1)(x+1+h)
= h/h * -1/(x+1)(x+1+h)
--> -1/(x+1)^2