whats the derivative of 1/1 +(x^2)?

Answer 1

A) If you're advanced enough in mathematics to ask for a derivative, you must also know PEMDAS, the order in which basic arithmetic operations should be performed.

In that case, you will know that the PRECISE mathematical interpretation of the expression you have written is:

1/1 +(x^2) = 1 + x^2.

That being so, its derivative with respect to x is 2x.

(And its derivative with respect to x^2 is 1!)

B) HOWEVER, it seems probable that you MEANT to write your original expression as:

1/(1 + x^2).

If so, you really need to put some effort into writing your mathematics clearly. It will greatly aid your communication.

By the chain rule, the derivative of this latter function with respect to x is given by:

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

Live long and prosper.

Answer 2

I assume everything past the / is supposed to be in the denominator?

Rewrite it like this:
(1 + x^2)^-1

Use the power rule, and the chain rule

Answer 3

y=1/(1+x^2)
y=(1+x^2)^-1
y'=-1(1+x^2)^-2 *2x
y'=-2x/(1+x^2)

Answer 4

-2x/(1+2x^2+x^4) or -2x/[(1+x^2)^2]