#1**+5 **

Possible derivation:

d/dx(1/(1 + x^2))

Using the chain rule, d/dx(1/(x^2 + 1)) = d/( du)1/u 0, where u = x^2 + 1 and ( d)/( du)(1/u) = -1/u^2:

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

Differentiate the sum term by term:

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

The derivative of 1 is zero:

= -(d/dx(x^2) + 0)/(1 + x^2)^2

Simplify the expression:

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

Use the power rule, d/dx(x^n) = n x^(n - 1), where n = 2: d/dx(x^2) = 2 x:

**Answer: |= -2x / (1 + x^2)^2 **

Guest Mar 16, 2017