已知z=z(x,y)由sin(xy)+z^2=sin(x+z)確定,求z關於x的偏導數

已知z=z(x,y)由sin(xy)+z^2=sin(x+z)確定,求z關於x的偏導數

sin(xy)+z^2=sin(x+z)
ycos(xy)+2z(δz/δx)= [ 1+(δz/δx)] cos(x+z)
[2z - cos(x+z)](δz/δx)= cos(x+z)- ycos(xy)
δz/δx = [cos(x+z)- ycos(xy)]/[2z - cos(x+z)]