Find the derivative of x at x = 1.
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.
Let the given function be:
The derivative of the given function at
From the definition, derivative of a function
Here, the value of
On solving the value of
On further simplification, we get
Thus, the derivative of the function
