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Let y be an implicit function of x defi...

Let y be an implicit function of x defined by `x^(2x)-2x^(x) cot y-1=0`. Then y' (1) equals

A

-1

B

1

C

`log2`

D

`-log2`

Text Solution

Verified by Experts

The correct Answer is:
A
We have,
`x^(2x)-2x^(x)coty-1=0" "…(i)`
When x=1, we get
`1-2coty-1=0impliescoty=0impliesy=(pi)/(2)`
Differentiating (i) w.r. to x, we get
`2x^(2)(1+logx)-2x^(x)(1+logx)coty+2x^(x)cosec^(2)y(dy)/(dx)=0`
Putting `x=1, y=(pi)/(2),` we get
`2-2xx0+2(dy)/(dx)=0implies(dy)/(dx)=-1`
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