# Mark the correct alternative in each of the following: If f ( x ) = x n − a n x − a then f ′ ( a ) - Mathematics

MCQ

Mark the correct alternative in each of the following:

If$f\left( x \right) = \frac{x^n - a^n}{x - a}$ then $f'\left( a \right)$

#### Options

•  1

•  0

• $\frac{1}{2}$

• does not exist

#### Solution

Given:

$f\left( x \right) = \frac{x^n - a^n}{x - a}$

Now, f(x) is not defined at x = a. Therefore, f(x) is not differentiable at x = a. $f'\left( a \right)$ does not exist.
Hence, the correct answer is option (d).

Concept: The Concept of Derivative - Algebra of Derivative of Functions
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 30 Derivatives
Q 11 | Page 48