# How do you use the limit definition of the derivative to find the derivative of #f(x)=x+1#?

##### 1 Answer

Feb 1, 2017

# f'(x) = 1 #

#### Explanation:

The definition of the derivative of

# f'(x)=lim_(h rarr 0) ( f(x+h)-f(x) ) / h #

So if

# \ \ \ \ \ f(x+h) = (x+h) + 1 #

# :. f(x+h) = x+h + 1 #

And so the derivative of

# \ \ \ \ \ f'(x) = lim_(h rarr 0) ( (x+h + 1) - (x+1) ) / h #

# " " = lim_(h rarr 0) ( x+h + 1 -x-1 ) / h #

# " " = lim_(h rarr 0) ( h ) / h #

# " " = lim_(h rarr 0) 1 #

# " " = 1 #