Question

Найти dz/dx и dz/dy функции:  

z=e^xy+ln(x+ln y)

Answer 1

$z=e^xy+ln(x+ln y);$
$frac{dz}{dx}=(e^xy+ln(x+ln y))'_x=e^xy+ frac{1}{x+ln y};$
$frac{dz}{dy}=(e^xy+ln(x+ln y))'_y=e^x+ frac{ (lny)'_y }{x+ln y}=e^x+ frac{ 1}{y(x+ln y)};$