Question

U=ln (x^2+y^2)
найти деференциал

Answer 1

$dz(x,y)= frac{partial z(x,y)}{partial x} dx+ frac{partial z(x,y)}{partial y} dy=$
$=(ln(x^2+y^2))'_xdx+ (ln(x^2+y^2))'_ydy=$
$= frac{(x^2+y^2)'_x}{x^2+y^2} dx+ frac{(x^2+y^2)'_y}{x^2+y^2} dy=$
$= frac{2x}{x^2+y^2} dx+ frac{2y}{x^2+y^2} dy$