CLASS_11_MATHS_SOLUTIONS_NCERT

Class XI Chapter 13 – Limits and Derivatives Maths
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2
f x x a b x ab
d 2
f ' x x a b
x ab
dx
d 2 d d
x a b x
ab
dx dx dx
d n n 1
On using theorem x nx
,we obtain
dx
f ' x 2x a b 0 2x a b
2
( ii)Let
f x ax b
f x a x 2abx b
2 4 2 2
2
d d d d
f ' x a x 2abx b a x 2ab x b
dx dx dx dx
d n n 1
On using theorem x nx
,we obtain
dx
2 4 2 2 2 4 2 2
2 3 2
f'(x)= a 4x 2ab 2x b 0
2 3
4a x 4
4ax ax
Let f () x
2
abx
b
xa
xb
d x a
f ' x
dx
x b
By quotient rule,
d
x b x ax a x b
dx
dx
xb 2
x b1 x a1
2
xb
f' x
x b x a
2
xb
ab
xb
2
d
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