Question

f(x,y)=x^y найти df(e;2)

Answer 1

Ответ:   №3 .

$f(x;y)=x^{y}\\\\f'_{x}=y\cdot x^{y-1}\ \ \ ,\ \ \ f'_{y}=x^{y}\cdot lnx\\\\df(x;y)=y\cdot x^{y-1}\, dx+x^{y}\cdot lnx\, dy\\\\df(e;2)=2\cdot e^1\, dx+e^2\cdot lne\, dy=2e\, dx+e^2\, dy$