Question

Помогите с производной!

Answer 1

f'=-e^(1-x)sinПx/2+e^(1-x)cosПx/2*П/2=П/2e^(1-x)(cosПx/2-2/ПsinПx/2)
f'(1)=П/2e^0(cosП/2-2/ПsinП/2)=П/2(1-2/П)=П/2-1

Answer 2

$f(x)=e^{1-x}*sin frac{pi*x}{2}$
$f'(x)=(e^{1-x}*sin frac{pi*x}{2})'=\\(e^{1-x})'*sin frac{pi*x}{2}+e^{1-x}*(sin frac{pi*x}{2})'=\\e^{1-x}*(-1)*sin frac{pi*x}{2}+e^{1-x}*cos frac{pi*x}{2}*frac{pi}{2}=\\e^{1-x}(frac{pi}{2}cos frac{pi*x}{2}-sin frac{pi*x}{2}$

$f'(1)=e^{1-1}*(frac{pi}{2}*cos frac{pi*1}{2}-sin frac{pi*1}{2})=\\1*(frac{pi}{2}*0-1)=-1$