1. Tardigrade
  2. Question
  3. Mathematics
  4. If x=ey+ey+......to ∞ ,x>0, the (dy/dx) is

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. If $ x={{e}^{y+{{e}^{y+......to\,\infty }}}},x>0, $ the $ \frac{dy}{dx} $ is

JamiaJamia 2007

Solution:

$ x={{e}^{y+{{e}^{y+.....\infty }}}} $ $ \therefore $ $ x={{e}^{y+x}} $ Taking log on both sides, we get $ \log x=(y+x) $ Differentiate w.r. to $ x, $ we get $ \frac{1}{x}=\frac{dy}{dx}+1\Rightarrow \frac{dy}{dx}=\frac{1-x}{x} $