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Chapter 13 Limits and Derivatives Ex 13.2 Solutions

Question - 1 : - Find the derivative of x2– 2 at x = 10

Answer - 1 : -

Let f (x) = x2 –2

Question - 2 : - Find the derivative of x at x = 1.

Answer - 2 : -

Let f (x) = x
Then,

Question - 3 : - Find the derivative of 99x at x = l00.

Answer - 3 : -

Let f (x) = 99x,
From first principle
=99

Question - 4 : -

Find the derivativeof the following functions from first principle

(i) x3 –27

(ii) (x – 1) (x – 2)

(iii) 1 / x2

(iv) x + 1 / x – 1

Answer - 4 : -

(i) Let f (x) = x3 –27

From first principle

(ii) Let f (x) = (x – 1) (x – 2)

From first principle

(iii) Let f (x) = 1 / x2

From first principle, we get

(iv) Let f (x) = x + 1 / x – 1

From first principle, we get

Question - 5 : - For the function   .Prove that f’ (1) =100 f’ (0).

Answer - 5 : -


Question - 6 : - Find the derivative of   for some fixed real number a.

Answer - 6 : -


Question - 7 : -

For some constantsa and b, find the derivative of
(i) (x − a) (x − b)

(ii) (ax2 +b)2

(iii) x – a / x – b

Answer - 7 : -

(i) (x – a) (x – b)

(ii) (ax2 + b)2

= 4ax (ax2 + b)

(iii) x – a / x – b

Question - 8 : - Find the derivative of   for some constant a.

Answer - 8 : -


Question - 9 : -

Find the derivativeof

(i) 2x – 3 / 4

(ii) (5x3 +3x – 1) (x – 1)

(iii) x-3 (5+ 3x)

(iv) x5 (3– 6x-9)

(v) x-4 (3– 4x-5)

(vi) (2 / x + 1) – x2 / 3x – 1

Answer - 9 : -

(i)

(ii)

(iii)

(iv)

(v)

(vi)

Question - 10 : - Find the derivative of cos x from first principle

Answer - 10 : -


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