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NCERT Class XI Mathematics - Limits and Derivatives - Solutions

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Question : 69
Total: 72
4x+5sinx
3x+7cosx
Solution:  
Let f (x) =
4x+5sinx
3x+7cosx
 ... (i)
Differentiating (i) with respect to x, we get
d
dx
 [f (x)] =
(3x+7cosx)(4x+5sinx)′−(4x+5sinx)(3x+7cosx)′
(3x+7cosx)2

=
(3x+7cosx)(4+5cosx)−(4x+5sinx)(3−7sinx)
(3x+7cosx)2

=
12x+15xcosx+28cosx+35[cos2x+sin2x]−12x+28xsinx−15sinx
(3x+7cosx)2

=
35+15xcosx+28cosx+28xsinx−15sinx
(3x+7cosx)2

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