Interesting problem

[pollyshearead]

How should I start?
find y'
x^√y = y^√x

 

[skeeter]

[MATH]\ln[/MATH] denotes the natural log, base [MATH]e[/MATH] ...

assuming [MATH]y[/MATH] is an implicit function of [MATH]x[/MATH]
[MATH]\dfrac{d}{dx}\bigg[\sqrt{y} \cdot \ln{x} = \sqrt{x} \cdot \ln{y}\bigg][/MATH]
product rule in concert with the chain rule, then isolate [MATH]y'[/MATH]

 

[pollyshearead]

(1/2)(y)^(-1/2) • 1/ (dy/dx)

Would this be the left side?

 

[Deleted member 4993]

(1/2)(y)^(-1/2) • 1/ (dy/dx)

Would this be the left side?

No

\(\displaystyle \frac{d}{dx} [ \sqrt{y} * ln(x)]\)

= \(\displaystyle \frac{1}{2} * \frac{1}{\sqrt{y}} * \frac{dy}{dx} * ln(x) \ + \sqrt{y} * \frac{1}{x}\)