Find the derivative of 99 x at x = 100.
Let the given function be:
f ( x ) = 99 x
We have to find the derivative of the given function at x = 100
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 = 100
On solving the value of f ( x ) , we get
f ' ( x ) = lim h → 0 f ( 100 + h ) − f ( 100 ) h = lim h → 0 99 ( 100 + h ) − 99 ( 100 ) h = lim h → 0 9900 + 99 h − 9900 h = lim h → 0 99 h h
On further simplification, we get
f ' ( x ) = 99
Thus, the derivative of the function f ( x ) = 99 x at x = 100 is 99.
Let the given function be:
We have to find 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
