NCERT Class XI Mathematics - Limits and Derivatives - Solutions

Question : 40

Total: 72

Find the derivative of

xn−an

x−a

for some constant a.

Solution:

Let f (x) =

xn−an

x−a

........(i), where a is a constant.
Differentiating (i) with respect to x, we get
f' (x) =

(x−a)(xn−an)′−(xn−an).(x−a)′

(x−a)2

⇒ f' (x) =

(x−a)(nxn−1−0)−(xn−an).(1)

(x−a)2

⇒ f' (x) =

nxn−1(x−a)−xn+an

(x−a)2

nxn−anxn−1−xn+an

(x−a)2

∴ f' (x) =

nxn−anxn−1−xn+an

(x−a)2

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