viii) sin\displaystyle ^{2}{ln(cosecx)} কে x এর সাপেক্ষে অন্তরীকরণ করে পাই,

CALCULAS _img

viii) sin\displaystyle ^{2}{ln(secx)}
মনে করি,
y=sin\displaystyle ^{2}{ln(secx)}
x এর সাপেক্ষে অন্তরীকরণ করে পাই,
\displaystyle \frac{dy}{dx}=\displaystyle \frac{d}{dx} [sin{ln(cosecx)}]\displaystyle ^{2}

=2 sin{ln(cosecx)}sin{ln(cosecx)}\displaystyle cos{ln( cosecx).\displaystyle \frac{1}{cosecx}\displaystyle \frac{d}{dx}(cosecx)

=2 sin{ln(cosecx)}sin{ln(cosecx)}\displaystyle cos{ln( cosecx).\displaystyle \frac{1}{cosecx}.(-cosecx.cotx)

=2 sin{ln(cosecx)}sin{ln(cosecx)}\displaystyle cos{ln( cosecx).(-cotx)

= -cotx sin{2ln(cosecx)} (ans):

Post Author: showrob

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