Find the derivative of (xⁿ - aⁿ)/(x - a) for some constant a

Solution:

Let f (x) = (xn - an)/(x - a)

f' (x) = d/dx [(xn - an)/(x - a)]

By quotient rule,

f' (x) = [(x - a) d/dx (xn - an) - (xn - an) d/dx (x - a)] / ( x - a)2

= [(x - a)(nxn - 1 - 0) - (xn - an)]/(x - a)2

= (nxn - anxn-1 - xn + an)/(x - a)2

NCERT Solutions Class 11 Maths Chapter 13 Exercise 13.2 Question 8

Find the derivative of (xⁿ - aⁿ)/(x - a) for some constant a

Summary:

The derivative of (xn - an)/(x - a) is (nxn - anxn-1 - xn + an)/(x - a)2

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