` "tan"^(-1)x` – InterviewSolution

InterviewSolution

1.	` "tan"^(-1)x`
Answer» Let `y= "tan"^(-1)x` `implies (dy)/(dx)=(d)/(dx)"tan"^(-1)x=(1)/(1+x^(2))` `implies (d^(2)y)/(dx^(2))=(d)/(dx)((1)/(1+x^(2)))=(d)/(dx)(1+x^(2))^(-1)` `= -(1+x^(2))^(-2)*(d)/(dx)(1+x^(2))` `= -(2x)/((1+x^(2))^(2))`

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