Question

If y = √x^√x^√x...... then dy/dx​

Answer 1

Step-by-step explanation:

1. $y = \sqrt{x}^{y}$
2. $ln(y) = y ln( {x}^{ \frac{1}{2} } )$
3. $\frac{1}{y} \frac{dy}{dx} = \frac{y}{2x} + \frac{1}{2} ln(x) \frac{dy}{dx}$
4. $( \frac{1}{y} - \frac{1}{2} ln(x)) \frac{dy}{dx} = \frac{y}{2x}$
5. $\frac{dy}{dx} = \frac{y}{2x( \frac{1}{y } - \frac{1}{2} ln(x)) }$