Continuity and Differentiability — Maths STD 12 Science — Question

$\therefore \frac{{dy}}{{dx}} = \frac{1}{{\cos {e^x}}}\frac{d}{{dx}}\left( {\cos {e^x}} \right)\,\,\left[ {\because \frac{d}{{dx}}\log f\left( x \right) = \frac{1}{{f\left( x \right)}}\frac{d}{{dx}}f\left( x \right)} \right]$

$= \frac{1}{{\cos {e^x}}}\left( { - \sin {e^x}} \right)\frac{d}{{dx}}{e^x}\,\,\left[ {\because \frac{d}{{dx}}\cos f\left( x \right) = - \sin f\left( x \right)\frac{d}{{dx}}f\left( x \right)} \right]$

= - (tane^x)e^x = -e^x (tan e^x)