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Question
Y
=
ln
cot
tan
-
1
x
2
হলে
dy
dx
-
1
x
2
x
-x
1
x
ANSWER : 1
Descrption
<p><strong>y</strong>=ln cot tan<sup>-1</sup> x/2</p><p>Y=ln cot cot<sup>_1</sup> 2/x ( tan<sup>-1</sup> a=cot<sup>-1</sup> 1/a)</p><p>Y=ln 2/x ( cotcot<sup>-1</sup> a= a)</p><p>=><strong>dy<sub>/dx </sub></strong> = 1<sub>/(2/x)</sub> × dy<sub>/dx </sub> ( 2/x)</p><p>=><strong>dy<sub>/dx </sub></strong> = x<sub>/2 </sub> × 2 × <strong>dy<sub>/dx </sub></strong> x<sup>-1 </sup></p><p>=><strong>dy<sub>/dx </sub></strong> = x<sub>/2 </sub> × 2 ×(-1)× 1<sub>/x<sup>2 ( </sup></sub><strong>dy<sub>/dx </sub></strong> x<sup>n </sup> =x<sup>n-1 </sup></p><p>=><strong>dy<sub>/dx </sub></strong> = <strong>-2x<sub>/2x<sup>2</sup></sub></strong></p><p>=><strong>dy<sub>/dx </sub></strong> = -1<sub>/</sub><strong><sub>x</sub></strong></p><p>An's: -1<sub>/</sub><strong><sub>x</sub></strong></p>
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