Question

if f(x)=x cot x, then f'(1) is

Answer 1

Answer:

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Question

If f(x)=cot

−1

(

2

x

x

−x

−x

), then f

′

(1) equals

A

−1

B

1

C

log2

D

−log2

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Solution

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Correct option is A)

Substitute u=x

x

and using logarithmic differentiation. we get logu=xlogx,

⇒

u

1

dx

du

=x

x

1

+logx ⇒

dx

du

=x

x

(1+logx)

Similarly, if v=x

−x

, we get

dx

dv

=−x

−x

(1+logx)

∴ f

′

(x)=−

1+(

2

x

x

−x

−x

)

2

1

dx

d

(

2

x

x

−x

−x

)

=−

x

2x

+x

−2x

+2

4

[

2

1

[(x

x

+x

−x

)(1+logx)]]

⇒ f

′

(1)=−

1+1+2

2

[2(1+log1)]=−1

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