1.

If `(d(f(x))/(dx)=(1)/(1+x^(2)) `then `(d)/(dx){f(x^(3))} `isA. `(3x)/(1+x^(3))`B. `(3x^(2))/(1+x^(6))`C. `(-6x^(5))/((1+x^(6))^(2))`D. `(-6x^(5))/(1+x^(6))`

Answer» Correct Answer - 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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