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Question

Find the derivative of 99 x at x = 100.

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Solution

Let the given function be:

f( x )=99x

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

Here, the value of a=100

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

f ' ( x )= lim h0 f( 100+h )f( 100 ) h = lim h0 99( 100+h )99( 100 ) h = lim h0 9900+99h9900 h = lim h0 99h h

On further simplification, we get

f ' ( x )=99

Thus, the derivative of the function f( x )=99x at x=100 is 99.


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