How do you find the derivative of f(x)= 2/(1+x^2) ?

1 Answer
Oct 29, 2016

y=f(x)

y=2/(1+x^2)

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

2y^-1=1+x^2

Now use implicit differentiation...

-2y^-2*(dy)/(dx)=2x

-2/(y^2)*(dy)/(dx)=2x

Divide expressions on both sides of the equation by 2...

-1/y^2*(dy)/(dx)=x

Multiply expressions on both sides of the equation by -1...

1/y^2*(dy)/(dx)=-x

Now multiply expressions on both sides of the equation by y^2...

(dy)/(dx)=-x*y^2

Don't forget the real value of y...

(dy)/(dx)=-x*(2/(1+x^2))^2

Clean up the final result...

(dy)/(dx)=-(4x)/((1+x^2)^2)

Which means that...

f'(x)=-(4x)/((1+x^2)^2)