Question

已知z=f(xy,x^2+y^2),求az/ax

Answer 1

令f1(x,y)=x*y; f2(x,y)=x^2+y^2;

az/ax=[аf(f1(x,y),f2(x,y))/аx]*(аf1(x,y)/аx)+[аf(f1(x,y),f2(x,y))/аy]*(аf2(x,y)/аx)

=[аf(xy,x^2+y^2)/аx]*y+[аf(xy,x^2+y^2)/аy]*2*x

=y*[аf(xy,x^2+y^2)/аx]+2*x*[аf(xy,x^2+y^2)/аy]