Question

if y=x+1/x then prove that x²=dy/dx -xy+2=0

Answer 1

Answer:

Y=x^x Taking log on both sides log y=log x^x log y=x logx (1/y)(dy/dx)=(x*1/x)+logx (dy/dx)=y(1+log x) d/dx(dy/dx)=d/dx(y(1+logx)) d^2y/dx^2=(1+log x)(dy/dx)+y/x Now, 1/y(dy/dx)^2=(1/y)*y^2(1+logx)^2 Therefore d^2y/dx^2-1/y(dy/dx)^2-y/x=(1+log x)dy/dx - y(1+log x)^2 +y/x - y/x = (1+log x)(1+log x) * y - y(1+log x)^2 =y(1+log x)^2 - y(1+log x)^2 =0=RHS[PROVED]

Step-by-step explanation:

Hii, Follow N Brainliest me!!!