求函数z=(x+y)sin(x-y)的偏导数∂z/∂x,∂z/∂y
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求函数z=(x+y)sin(x-y)的偏导数∂z/∂x,∂z/∂y
求函数z=(x+y)sin(x-y)的偏导数∂z/∂x,∂z/∂y
求函数z=(x+y)sin(x-y)的偏导数∂z/∂x,∂z/∂y
∂z/∂x只对x求导数,而把y看作一个常数,∂z/∂x=(x+y)'sin(x-y)+(x+y)sin(x-y)'=
sin(x-y)+(x+y)cos(x-y)
∂z/∂y只对y求导数,而把x看作一个常数,∂z/∂y=(x+y)'sin(x-y)+(x+y)sin(x-y)'
=sin(x-y)+(x+y)[-cos(x-y)]
=sin(x-y)-(x+y)cos(x-y)
∂z/∂x=sin(x-y)+(x+y)cos(x-y)
∂z/∂y=sin(x-y)-(x+y)cos(x-y)
diff((x+y)*sin(x-y), x) = (diff(x+y, x))*sin(x-y)+(x+y)*(diff(sin(x-y), x)) and (diff(x+y, x))*sin(x-y)+(x+y)*(diff(sin(x-y), x)) = (diff(x, x)+diff(y, x))*sin(x-y)+(x+y)*(diff(sin(x-y), x)) and (diff(x, x)+diff(y, x))*sin(x-y)+(x+y)*(diff(sin(x-y), x)) = (diff(x, x))*sin(x-y)+(x+y)*(diff(sin(x-y), x)) and (diff(x, x))*sin(x-y)+(x+y)*(diff(sin(x-y), x)) = sin(x-y)+(x+y)*(diff(sin(x-y), x)) and sin(x-y)+(x+y)*(diff(sin(x-y), x)) = sin(x-y)+(eval((x+y)*(diff(sin(_X), _X)), _X = x-y))*(diff(x-y, x)) and sin(x-y)+(eval((x+y)*(diff(sin(_X), _X)), _X = x-y))*(diff(x-y, x)) = sin(x-y)+(eval((x+y)*(diff(sin(_X), _X)), _X = x-y))*(diff(x, x)+diff(-y, x)) and sin(x-y)+(eval((x+y)*(diff(sin(_X), _X)), _X = x-y))*(diff(x, x)+diff(-y, x)) = sin(x-y)+(eval((x+y)*(diff(sin(_X), _X)), _X = x-y))*(diff(x, x)) and sin(x-y)+(eval((x+y)*(diff(sin(_X), _X)), _X = x-y))*(diff(x, x)) = sin(x-y)+eval((x+y)*(diff(sin(_X), _X)), _X = x-y) and sin(x-y)+eval((x+y)*(diff(sin(_X), _X)), _X = x-y) = sin(x-y)+(x+y)*cos(x-y) diff(sin(x-y), y) = (eval(diff(sin(_X), _X), _X = x-y))*(diff(x-y, y)) and (eval(diff(sin(_X), _X), _X = x-y))*(diff(x-y, y)) = (eval(diff(sin(_X), _X), _X = x-y))*(diff(x, y)+diff(-y, y)) and (eval(diff(sin(_X), _X), _X = x-y))*(diff(x, y)+diff(-y, y)) = (eval(diff(sin(_X), _X), _X = x-y))*(diff(-y, y)) and (eval(diff(sin(_X), _X), _X = x-y))*(diff(-y, y)) = -(eval(diff(sin(_X), _X), _X = x-y))*(diff(y, y)) and -(eval(diff(sin(_X), _X), _X = x-y))*(diff(y, y)) = -(eval(diff(sin(_X), _X), _X = x-y)) and -(eval(diff(sin(_X), _X), _X = x-y)) = -cos(x-y) 过程有点复杂,我今天的图片上传功能用完了,没法给你传图片,只能这样子的格式了。希望对你有帮助。