\(\frac{d}{d x}\left(e^{\log _e \sqrt{1+\tan ^2 x}}\right)=\)

\(\frac{d}{d x}\left(e^{\log _e \sqrt{1+\tan ^2 x}}\right)=\)
  1. \(\sec ^2(x) \cdot \tan (x)\)
  2. \(\sec (x) \cdot \tan ^2(x)\)
  3. \(\sec (x) \cdot \tan (x)\)
  4. \(\tan ^2(x)\)

Solution

\(\frac{d}{d x}\left(e^{\log _e} \sqrt{1+\tan ^2 x}=\frac{d}{d x}(\sec x)=\sec x \tan x\right.\).

Asked in: AP EAMCET 2020 (18 Sep Shift 1)

Practice more Differentiation questions on Aicharya