求y'和dy/dx的平方

Question

如题所述

Answer 1

5.对4x^2+2x+xy=2求导得
8x+2+y+xy'=0,
∴在x=2,y=-9时18-9+2y'=0,y'=-9/2.
所求切线方程是y+9=(-9/2)(x-2),即y=-9x/2.
6.xcosy=3y,
求导得cosy-xsiny*y'=3y',
cosy=(3+xsiny)y',
y'=cosy/(3+xsiny),
再求导得y''=[-(3+xsiny)siny*y'-(siny+xcosy*y')cosy]/(3+xsiny)^2
=-[(3siny+x)y'+sinycosy]/(3+xsiny)^2
=-[(3siny+x)cosy+(3+xsiny)sinycosy]/(3+xsiny)^3
=-[6sinycosy+xcosy+x(siny)^2*cosy]/(3+xsiny)^3,为所求。