Question

设方程In√x2+y2=arctan y/x确定函数y=y(x)，求dy/dx？请直接给出步骤

Answer 1

问：设方程In√x2+y2=arctan y/x确定函数y=y(x)，求dy/dx？请直接给出步骤

答：即0.5ln(x^2+y^2)=arctan(y/x) 对x求导得到0.5(2x+2y*y')/(x^2+y^2)= 1/(1+y^2/x^2) *(y/x)' 即(2x+2y*y')/(x^2+y^2)=2x^2/(x^2+y^2) *(x *y'-y)/x^2 于是 x+y*y'=2(x *y'-y) 即(2x-y)*y'=x+2y 所以 dy/dx=(x+2y)/(2x-y)