1..[f(e^2x)]'=f'(e^2x)*(e^2x)*2=2e^2xf‘(e^2x)
2.∫(x-1)/(1-√x)dx
令√x=t；t²=x；2tdt=dx；
∫(x-1)/(1-√x)dx
=∫2t(t²-1)/(1-t)dt
=-2∫t(t+1)dt
=-2[t^3/3+t²/2+C]
=-2x√x/3-x+C
3.y^5+2y-x-3x^7=0
令x=0,得到y=0
两边微分
4y^4dy+2dy-dx-21x^6dx=0
令x=0,y=0得到
2dy-dx=0
dy/dx=1/2 就是在x=0的导数值
4.y=(x^lny)+1
变形得到lnxlny=ln(y-1)
两边微分
1/x*lnydx+1/y*lnxdy=1/(y-1)*dy
⇒dy/dx=(lny/x)/[1/(y-1)-lnx/y]
=[y(y-1)lny]/[xy-(y-1)xlny]