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If y=(x^(2))/((x+1))"then"(dy)/(dx)"is":...

If `y=(x^(2))/((x+1))"then"(dy)/(dx)"is":-`

A

`(x(3x+2))/((x+1)^(2))`

B

`(-x(x+2))/((x+1)^(2))`

C

`(x(x+2))/((x+1)^(2))`

D

`(x(x+2))/((x+1))`

Text Solution

Verified by Experts

The correct Answer is:
C
`y=u/v `
` (dy)/(dx) =(v(du)/(dx)-u(dv)/(dx))/(v^(2))u=x^(2)`
`v=(x+1)`
`=((x+1)(d)/(dx)(x)^(2)-x^(2) (d)/(dx)(x+1))/((x+1)^(2))`
`=(2x(x+1)-x^(2))/((x+1)^(2))=(x(x+2))/((x+1)^(2))`
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