Question

Question 8 Find the derivative of (x^n- a^n) / (x-a) for some constant a.

Class XI - Limits and Derivatives Page 313

Answer 1

apply the product rule here

f(x) = xⁿ-aⁿ/x-a
f'(x) = (x-a) d/dx(xⁿ-aⁿ) - (xⁿ-aⁿ)d/dx(x-a)/(x-a)²
=> (x-a) ( nxⁿ-¹) - (xⁿ-aⁿ)(1)/(x-a)²
=> (n-1)xⁿ - naxⁿ-1 +aⁿ/(x-a)²

I hope this will help you .
ask me if you will face any problem.

Answer 2

Let f(x) = x^n-a^n/x-a

f'(x) = d/DX (x^n-a^n/x-a)

By Quotient Rule

f'(x)= (x-a)d/dx(x^n-a^n)-(x^n-a^n)d/dx(x-a)÷(x-a)^2

= (x-a)(nx^n-¹ -0)- (x^n-a^n)÷(x-a)^2

f'(x)= (x-a) (nx^n-¹ -0)(x^n-a^n)÷(x-a)^2

f'(x)= nx^n - anx^n-¹ -x^n+ a^n÷(x-a)^2