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If y="cosec"(cot^(-1)x), then (dy)/(dx) ...

If `y="cosec"(cot^(-1)x),` then `(dy)/(dx)` at `x=1` is equal to: `1/(sqrt(2))` (b) `1/2` (c) 1 (d) `sqrt(2)`

Text Solution

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`g'(x)=2[f(2f(x)+2)][(d)/(dx)(f(2f(x)+2))]`
`=2[f(2f(x)+2)][f'(2+f(x)+2)xx2f'(x)]`
`rArr" "g'(0)=2f(2f(0)+2)f'(2f(0)+2)2f'(0)`
`=4f(0)[f'(0)]^(2)`
`4(-1)(1)=-4`
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