NCERT Class XI Mathematics - Limits and Derivatives - Solutions
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Question : 39
Total: 72
For some constants a and b, find the derivative of
(i) (x – a)(x – b)
(ii)( a x 2 + b ) 2
(iii)
(i) (x – a)(x – b)
(ii)
(iii)
Solution:
(i) Let f(x) = (x – a) (x – b) ... (1)
Differentiating (1) with respect to x, we get
f ′(x) = (x – a) (x – b)′ + (x – a)′ (x – b)
⇒ f ′(x) = (x – a) + (x – b) = 2x – a – b
(ii) Let f(x) =( a x 2 + b ) 2
Differentiating (1) with respect to x, we get
f ′(x) =2 ( a x 2 + b ) ( a x 2 + b )
(iii) Let f (x) =
Differentiating (1) with respect to x, we get
f' (x) =
=
Differentiating (1) with respect to x, we get
f ′(x) = (x – a) (x – b)′ + (x – a)′ (x – b)
⇒ f ′(x) = (x – a) + (x – b) = 2x – a – b
(ii) Let f(x) =
Differentiating (1) with respect to x, we get
f ′(x) =
(iii) Let f (x) =
Differentiating (1) with respect to x, we get
f' (x) =
=
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