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Question

Find the derivative of x at x = 1.

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Solution

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 h0 f( x+h )f ( a ) h

Here, the value of a=1

On solving the value of f ' ( x ) , we get

f ' ( x )= lim h0 f( 1+h )f( 1 ) h = lim h0 ( 1+h )1 h = lim h0 h h

On further simplification, we get

f ' ( x )=1

Thus, the derivative of the function f( x )=x at x=1 is 1.


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