Question

Determine a derivada da função f(x)= 1−√1+cos2(ex)

Answer 1

$\displaystyle \sf f(x) = 1-\sqrt{1+cos^2(e^{x})} \\\\ f(x) = 1-[1+cos^2(e^x)]^{\frac{1}{2}} \\\\\ Derivando : \\\\ f'(x) = -\frac{1}{2}\cdot [1+cos^2(e^x)]^{\left(\frac{1}{2}-1\right)}\cdot [[1+cos^2(e^x)]' \\\\\\ f'(x) = \frac{-1}{2}\cdot [1+cos^2(e^x)]^{\frac{-1}{2}}\cdot [2\cdot cos(e^{x})\cdot [-sen(e^{x})]\cdot e^{x}] \\\\\\ \boxed{\sf \ f'(x)= \frac{e^{x}\cdot cos(e^{x})\cdot sen(e^{x}) }{ \sqrt{1+cos^2(e^{x})}} \ }\checkmark$

item c