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If (d(f(x)))/(dx)=(1)/(1+x^(2)), then ...

If `(d(f(x)))/(dx)=(1)/(1+x^(2))`, then `(d)/(dx){f(x^(3))} `is

A

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

B

`(3x^(2))/(1+x^(6))`

C

`(-6x^(5))/((1+x^(6))^(2))`

D

`(-6x^(5))/(1+x^(6))`

Text Solution

Verified by Experts

The correct Answer is:
B
Given, `(d)/(dx){f(x)}=(1)/(1+x^(2))`
On integrating both sides, we get
`f(x)=tan^(-1)x`
`therefore" "(d)/(dx)f(x^(3))=(d)/(dx)(tan^(-1)x^(3))`
`=(1)/(1+(x^(3))^(2)).3x^(2)=(3x^(2))/(1+x^(6))`
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