Question

求:由方程所确定的隐函数的导数dy/dx?y=cos(x+y)

Answer 1

y = cos(x + y)

dy/dx = dcos(x + y)/d(x + y) · d(x + y)/dx,链式法则

dy/dx = - sin(x + y) · (1 + dy/dx)

dy/dx = - sin(x + y) - sin(x + y) · dy/dx

dy/dx · [1 + sin(x + y)] = - sin(x + y)

dy/dx = - sin(x + y)/[1 + sin(x + y)

dy/dx = - 1/[1 + csc(x + y)]