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Question
Find the second order derivative of the function.
tan–1 x
Solution
Let, y = tan-1x
Differentiating both sides with respect to x,
`dy/dx = d/dx tan^-1 x`
`= 1/((1 + x^2))`
Differentiating both sides again with respect to x,
`(d^2 y)/dx ^2 = d/dx (1 + x^2)^-1`
`= -1 (1 + x^2)^(-1 -1) d/dx (1 + x^2)`
`= - (1 + x^2)^-1 (2x)`
`= (-2x)/(1 + x^2)^2`
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