Final answer:
To find dx/dy, differentiate y with respect to x and then take the reciprocal.
Step-by-step explanation:
The question asks for the value of dx/dy if y = (1+x)/(1-x).
We can find the derivative dx/dy by differentiating y with respect to x and then taking the reciprocal.
- First, differentiate y with respect to x:
dy/dx = (1 - x) - (1 + x)(-1) / (1 - x)^2
- Next, take the reciprocal to find dx/dy:
dx/dy = 1 / [(1 - x) - (1 + x)(-1) / (1 - x)^2]
Therefore, dx/dy = (1 - x)^2 / [(1 - x) - (1 + x)] = (1 - x)^2 / (-2x)