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If y=ex⋅cot⁡x then dydx will be

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a

excot⁡x−cosec2⁡x

b

excosec2⁡x

c

excot⁡x−cosec2⁡x

d

excot⁡x

answer is C.

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Detailed Solution

y=excot⁡xdydx=exddxcot⁡x+cot⁡xdexdx ∵duvdx=udvdx+vdudx=ex−cosec2⁡x+cot⁡xex ∵ddxcot⁡x=−cosec2⁡xdexdx=ex=−cosec2⁡xex+excot⁡x

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If y=ex⋅cot⁡x then dydx will be