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The rate of change of sqrt(x^2+16) with ...

The rate of change of `sqrt(x^2+16)` with respect to `x/(x-1)` at `x=3` is

A

1

B

`(11)/(5)`

C

`-(12)/(5)`

D

`-3`

Text Solution

Verified by Experts

`u=sqrt(x^(2)+16)`
`therefore" "(du)/(dx)=(2x)/(2sqrt(x^(2)+16))=(x)/(sqrt(x^(2)+16))`
`v=(x)/(x-1)`
`rArr" "(dv)/(dx)=(-1)/((x-1)^(2))`
`therefore" "(du)/(dv)=(du//dx)/(dv//dx)=(-12)/(5)`
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