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If t(1+x^2)=x and x^2+t^2=y, then at x=2...

If `t(1+x^2)=x and x^2+t^2=y,` then at `x=2` the value of `(d y)/(d x)` is equal to Option 1. 24/5 Option 2: 101/125 Option 3: 488/155 Option 4: 358/125

A

`(24)/(5)`

B

`(101)/(125)`

C

`(488)/(155)`

D

`(358)/(125)`

Text Solution

Verified by Experts

The correct Answer is:
C
`(dy)/(dx)=2x+st.(dt)/(dx)`
Also, `t=(x)/(1+x^(2))`
`therefore" "(dt)/(dx)=(1-x^(2))/((1+x^(2))^(2))`
Now putting x = 2, we get
`(dt)/(dx)=(-3)/(25)`
`therefore" "(dy)/(dx)=2(2)+2((2)/(5)).(-3)/(25)=4-(12)/(125)=(488)/(125)`
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