Question

微积分 函数 隐函数，高数大神在哪

Answer 1

1、原式=∫f(arctanx)d(arctanx)=tan(arctanx)+C=x+C
2、原式=3*lim(x->0) [f(x0+3x)-f(x0)]/3x=3*f'(x0)=9
3、e^y*dy/dx+(1+dy/dx)/(x+y)=1
[e^y+1/(x+y)]*dy/dx=1-1/(x+y)
dy/dx=(x+y-1)/[(x+y)*e^y+1]
4、dz/dx=dz/du*du/dx+dz/dv*dv/dx
=e^u*sinv*y+e^u*cosv*1
=e^u*(sinv*y+cosv)
5、dz/dx=e^(xy^2)*y^2，dz/dy=e^(xy^2)*2xy
全微分dz=e^(xy^2)*y^2*dx+e^(xy^2)*2xy*dy
=e^(xy^2)*y*(ydx+2xdy)
6、原式=lim(x->0) (e^x-1-x)/x(e^x-1)
=lim(x->0) (e^x-1-x)/x^2
=lim(x->0) (e^x-1)/2x
=lim(x->0) x/2x
=1/2