The derivative of ax2+cot⁡x(p+qcos⁡x) is

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ax2+cot⁡x(−qsin⁡x)+(p+qcos⁡x)2ax−cosec2⁡x

ax2cot⁡x(qsin⁡x)+(p+qcos⁡x)2ax−cosec2⁡x

ax2cot⁡x(−qsin⁡x)+(p−qcos⁡x)2ax+cosec2⁡x

None of the above

answer is A.

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Detailed Solution

Let, y=ax2+cot⁡x(p+qcos⁡x)dydx=ax2+cot⁡xddx(p+qcos⁡x)+(p+qcos⁡x)ddxax2+cot⁡x =ax2+cot⁡x(0−qsin⁡x)+(p+qcos⁡x)2ax−cosec2⁡x=ax2+cot⁡x(−qsin⁡x)+(p+qcos⁡x)2ax−cosec2⁡x

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