Question

if x^x^x.....∞ then show that dy/dx = y² / x(1 - logy)​

Answer 1

This is the required solution.

Hope this helps you.

Answer 2

Answer:

dy/dx = y^2/x(1-y log x)

Step-by-step explanation:

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)

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