Calculus - Finding the equation for E (Elasticity of Demand)

[aarox95]

Find the equation for E, the Elasticity of Demand
P=100/(x^2+1)
I am using the formula E=(-p/x)*dx/dp
I got x=sqrt((100-p/p)) I am stuck formulating E from here
Please show steps if possible.
Thank you!!!

 

[DrPhil]

Find the equation for E, the Elasticity of Demand
P=100/(x^2+1)
I am using the formula E=(-p/x)*dx/dp
I got x=sqrt((100-p/p)) I am stuck formulating E from here
Please show steps if possible.
Thank you!!!

I would start with dp/dx, rather than finding x(p).

\(\displaystyle \displaystyle \dfrac{dp}{dx} = \dfrac{-100\ (2x)}{(x^2 + 1)^2}\)

Of course dx/dp is the inverse of that. How far will that get you?