(A) Let $f(x) = \frac{x^n - a^n}{x - a}$.Using the quotient rule,$\frac{d}{dx} \left( \frac{u}{v} \right) = \frac{v u' - u v'}{v^2}$,where $u = x^n -

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$\frac{(n-1)x^n - nax^{n-1} + a^n}{(x-a)^2}$

(A) Let $f(x) = \frac{x^n - a^n}{x - a}$.Using the quotient rule,$\frac{d}{dx} \left( \frac{u}{v} \right) = \frac{v u' - u v'}{v^2}$,where $u = x^n - a^n$ and $v = x - a$.$u' = n x^{n-1}$ and $v' = 1$.$f'(x) = \frac{(x - a)(n x^{n-1}) - (x^n - a^n)(1)}{(x - a)^2}$.$f'(x) = \frac{n x^n - n a x^{n-1} - x^n + a^n}{(x - a)^2}$.$f'(x) = \frac{(n - 1) x^n - n a x^{n-1} + a^n}{(x - a)^2}$.

Class 12 Mathematics Continuity and Differentiation Derivative at a point, Standard differentiation

Medium

Find the derivative of $\frac{x^{n}-a^{n}}{x-a}$ with respect to $x$,where $a$ is a constant.

A
$\frac{(n-1)x^n - nax^{n-1} + a^n}{(x-a)^2}$
B
$\frac{(n-1)x^n + nax^{n-1} - a^n}{(x-a)^2}$
C
$\frac{(n-1)x^n - nax^{n-1} - a^n}{(x-a)^2}$
D
$\frac{(n+1)x^n - nax^{n-1} + a^n}{(x-a)^2}$

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Derivative at a point, Standard differentiation

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Find the derivative of $\frac{x^{n}-a^{n}}{x-a}$ with respect to $x$,where $a$ is a constant.

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