1.设隐函数y=y(x)是由方程x=ln(x+y)所确定,试求dy/dx.2.设函数y=y(x)是由方程e^xy+y^3-5x=0所确定,试求dy/dx|x=0拜托步骤尽量详细点~~谢谢了
问题描述：
1.设隐函数y=y(x)是由方程x=ln(x+y)所确定,试求dy/dx.
2.设函数y=y(x)是由方程e^xy+y^3-5x=0所确定,试求dy/dx|x=0
拜托步骤尽量详细点~~谢谢了
答
1.对x=ln(x+y）求微分,得dx=(dx+dy)/(x+y),∴dy=(x+y-1)dx,∴dy/dx=x+y-1.2.e^(xy)+y^3-5x=0,①求微分得e^(xy)*(ydx+xdy)+3y^2*dy-5dx=0,∴[xe^(xy)+3y^2]dy=[5-ye^(xy)]dx,∴dy/dx=[5-ye^(xy)]/[xe^(xy)+3y^2].由①...