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NCERT Class XI Mathematics - Limits and Derivatives - Solutions

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Question : 60
Total: 72
sinx+cosx
sinx−cosx
Solution:  
Let f (x) =
sinx+cosx
sinx−cosx
 ... (i)
Differentiating (i) with respect to x, we get
d
dx
 (f (x)) =
(sinx−cosx)(sinx+cosx)′−(sinx+cosx)(sinx−cosx)′
(sinx−cosx)2

=
(sinx−cosx)(cosx−sinx)−(sinx+cosx)(cosx+sinx)
(sinx−cosx)2

=
sinxcosx−sin2x−cos2x+cosxsinx−[sinx+cosx]2
(sinx−cosx)2

=
−2
(sinx−cosx)2
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