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What is the second derivative of #1/(1+x^2)#?

1 Answer

Dec 12, 2016

#d^((2))/(dx^2) (1/(1+x^2)) = frac (6x^2-2) ((1+x^2)^3)#

Explanation:

#f(x) = 1/(1+x^2)#

Based on the chain rule:

#f'(x) = d/(dx) (1+x^2)^(-1) =(2x)(-1)(1+x^2)^(-2) = (-2x)/((1+x^2)^2)#

Using the quotient rule:

#f''(x) = frac ((-2)(1+x^2)^2 +2x*2x *2(1+x^2)) ((1+x^2)^4) = frac ((-2)(1+x^2) +8x^2) ((1+x^2)^3)= frac (6x^2-2) ((1+x^2)^3)#

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