Question

найти: f`(0),если f(x)=e^x*cosx

Answer 1

f '(x) = (e^x*cosx)' = e^(x*cosx) * (x*cosx)' = e^(x*cosx) * (x' * cosx + x* cos' x) = e^(x*cosx) * (cosx - x*sinx)

f '(0) = e^(0*cox0) * (cox0 - 0*sin0) = 1

Answer 2

f(x)=e^x*cosx;

 

$f'(x)=(e^x*cosx)'=$$(e^x)'cosx+e^x (cos x)'= e^x cos x-e^x sin x=e^x (cos x-sin x)$

 

$f'(0)=e^0 (cos 0-sin 0)=1*(1-0)=1*1=1$

ответ: 1