高数求切线和法线find the equations of tangent line and normal line of the_数学解答

高数求切线和法线
find the equations of tangent line and normal line of the curve X的立方+Y的立方—3XY=0 at the point (2开根号下3次方,4开根号下三次方）

人气：410 ℃　时间：2020-06-24 01:14:25

解答

x^2+y^3-3*x*y=0(x^2+y^3-3*x*y)'=0'2*x+2*y^2*y'-(3*y'*x+3*y)=0y'=(2*x-3*y)/(3*x-2*y^2)隐函数求导注：(y^3)'=y'*y*y+y*y'*y+y*y*y'y是一个函数,比如f(x).而x是自变量(x^3)'=3*x^2代入x,y即可法线,据互相垂直的直...