Question

if y=x^x^x..... then prove that. x dy/dx=y^2/1-y log x

Answer 1

y=x^x^x^... is an infinite series, so we can write y=x^y
Now, applying log base e on both sides;
logy=logx^y
logy=y*logx
Differentiating wrt x;
(1/y)*dy/dx = y(logx)' + y' logx

dy/dx = y( y/x + logx*dy/dx)
dy/dx - ylogx * dy/dx = y^2/x
dy/dx = y^2/x(1-ylogx)

Answer 2

Answer:

hope it helps you and don't forget to follow mè