Let the given function be:
f( x )=x
The derivative of the given function at x=1
From the definition, derivative of a function f( x ) over a point a can be written as:
f ' ( x )= lim h→0 f( x+h )−f ( a ) h
Here, the value of a=1
On solving the value of f ' ( x ) , we get
f ' ( x )= lim h→0 f( 1+h )−f( 1 ) h = lim h→0 ( 1+h )−1 h = lim h→0 h h
On further simplification, we get
f ' ( x )=1
Thus, the derivative of the function f( x )=x at x=1 is 1.
Find the derivative of f(x) = x at x = 1