Question

Обчисліть f '(π), якщо f(x)=x+tgx​

Answer 1

$f(x)=x+tgx\\\\f'(x)=x'+(tgx)'=1+\frac{1}{Cos^{2}x}\\\\f'(\pi)=1+\frac{1}{Cos^{2}\pi}=1+\frac{1}{(-1)^{2}}=1+1=2\\\\\boxed{f'(\pi)=2}$