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"If for "x in (0,(1)/(4))," the derivati...

`"If for "x in (0,(1)/(4))," the derivative of "tan^(-1)((6xsqrt(x))/(1-9x^(3)))" is "sqrt(x)cdotg(x),` then g(x) equals

A

`1//2`

B

1

C

`sqrt(2)`

D

`1sqrt(2)`

Text Solution

Verified by Experts

`y=sec(tan^(-1)x)`
`rArr" "(dy)/(dx)=sec (tan^(-1)x)cdottan (tan^(-1)x)cdot(1)/(1+x^(2))`
`rArr" "((dy)/(dx))_(x=1)=sec((pi)/(4))tan((pi)/(4))(1)/(1+1)=(1)/(sqrt(2))`
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