Question

y=x^y prove that xdy/dx=y^2/1-ylogx​

Answer 1

Answer:

sides;logy=logx^ylogy=y*logxDifferentiating wrt x;(1/y)*dy/dx = y(logx)' + y' logxdy/dx = y( y/x + logx*dy/dx)dy/dx - ylogx * dy/dx = y^2/x

y=x^x^x^... is an infinite series, so we can write y=x^yNow, applying log base e on both sides;logy=logx^ylogy=y*logxDifferentiating wrt x;(1/y)*dy/dx = y(logx)' + y' logxdy/dx = y( y/x + logx*dy/dx)dy/dx - ylogx * dy/dx = y^2/xdy/dx = y^2/x(1-ylogx) PLZ MARK ME AS BRAINLIEST ANSWER.