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

Options

A. 1
B. `(11)/(5)`
C. `-(12)/(5)`
D. `-3`

Answer

C

Explanation

`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)`