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Question
Find the second order derivative of the function.
tan–1 x
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Solution
Let, y = tan–1 x
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/((1 + x^2))`
= `((1 + x^2) d/dx (1) - (1) d/dx (1 + x^2))/(1 + x^2)^2`
= `((1 + x^2) xx 0 - 1 xx (0 + 2x))/(1 + x^2)^2`
= `(0 - 2x)/(1 + x^2)^2`
= `(-2x)/(1 + x^2)^2`
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