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iv) 2cosec 2xcos{ln(tanx)}
মনে করি,
y=2cosec 2xcos{ln(tanx)}
x এর সাপেক্ষে অন্তরীকরণ করে পাই,
\displaystyle \frac{dy}{dx}=\displaystyle \frac{d}{dx} 2cosec 2xcos{ln(tanx)}

=2[cosec2x\displaystyle \frac{d}{dx}cos{ln(tanx)}+cos{ln(tanx)}\displaystyle \frac{d}{dx}(cosec2x)}]
=2[cosec2x.(- sin{ln(tanx)}\displaystyle \frac{d}{dx}ln(tanx)+cos{ln(tanx)}(-cosec2x.cot2x\displaystyle \frac{d}{dx}(2x)

=2[cosec2x.(- sin{ln(tanx)}.\displaystyle \frac{1}{tanx}.\displaystyle \frac{d}{dx}(tanx)+cos{ln(tanx)}(-cosec2x).cot2x.2]

=2[cosec2x.(- sin{ln(tanx)}.\displaystyle \frac{1}{tanx}.sec\displaystyle ^{2}x -cos{ln(tanx)}(cosec2x.)cot2x.2]

Post Author: showrob

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