e的y次方+xy-e的x次方=0求dy/dx和dy/dxy的5次方+2y-x-3x的7次方=0求dy/dxx≠0上述；两题都是求方程所确定的隐函数的对数

Question

e的y次方+xy-e的x次方=0 求dy/dx 和 dy/dx y的5次方+2y-x-3x的7次方=0 求dy/dx x≠0
上述；两题都是求方程所确定的隐函数的对数

Answer 1

1.∵e^y+xy-e^x=0
==>e^y*y'+y+xy'-e^x=0
==>(e^y+x)y'=e^x-y
==>y'=(e^x-y)/(e^y+x)
∴dy/dx=y'=(e^x-y)/(e^y+x)；
2.∵y^5+2y-x-3x^7=0
==>5y^4*y'+2y'-1-21x^6=0
==>(5y^4+2)y'=1+21x^6
==>y'=(1+21x^6)/(5y^4+2)
∴dy/dx=y'=(1+21x^6)/(5y^4+2).