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If f(x)=cot−1⁡xx−x−x2 then f′(1)=

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a

−log2

b

log2

c

1

d

-1

answer is D.

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Detailed Solution

f′(x)=−11+xx−x−x22ddxxx−x−x2=4xx+x−x2xx(1+log⁡x)+x−x(1+log⁡x)2f′(1)=−4(1+1)21(1+log⁡1)+1(1+log⁡1)2=−1⋅1+12=−1.

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