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NCERT Class XI Mathematics - Limits and Derivatives - Solutions

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Question : 73
Total: 72
x
sinnx
Solution:  
Let f (x) =
x
sinnx
 ... (i)
Differentiating (i) with respect to x, we get
d
dx
 [f (x)] =
sinnx.1−x.nsinn−1xcosx
(sinnx)2
=
(sinx)n−1(sinx−nxcosx)
(sinx)2n
=
sinx−nxcosx
(sinx)2n−n+1
=
sinx−nxcosx
(sinx)n+1
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