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NCERT Class XI Mathematics - Limits and Derivatives - Solutions

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Question : 63
Total: 72
a+bsinx
c+dcosx
Solution:  
Let f (x) =
a+bsinx
c+dcosx
 ... (i)
Differentiating (i) with respect to x, we get
d
dx
 (f (x)) =
(a+bsinx)′(c+dcosx)−(a+bsinx)(c+dcosx)′
(c+dcosx)2

=
bcosx(c+dcosx)−(a+bsinx)(−dsinx)
(c+dcosx)2

=
bccosx+bdcos2x+adsinx+bdsin2x
(c+dcosx)2

=
bccosx+bd(cos2x+sin2x)+adsinx
(c+dcosx)2

=
bccosx+asdsinx+bd
(c+dcosx)2
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