What is the derivative of x to the power of infinity?

Dear Tanushi

 

y = x^x^x^x^-------infinitewe can write it-----y = x^ytaking log both sidelog y = log (x^y)log y = y log xtaking differentiation both side with respect to xd/dx (log y) = d/dx (y log x)1/y*dy/dx = y* d/dx(logx)+logx*dy/dx1/y*dy/dx = y / x+logx*dy/dxdy/dx (1/y - logx) = y/xdy/dx = y^2 / x(1 - y logx)