How do I Implicitly Differentiate this equation?

Question

My equation is $y=x^{y^2}$

I did the $\ln$ of both sides, then I tried implicit differentiation. I got $$y'= \frac{x^{y^2} y^2}{x}.$$

Answer 1

$$y=x^{y^2}$$ $$\ln y=y^2\ln x$$ $$\frac{1}{y}\cdot\frac{dy}{dx}=2y\frac{dy}{dx}\ln x+\frac{y^2}{x}$$

$$\left(\frac{1}{y}-2y\ln x\right)\frac{dy}{dx}=\frac{y^2}{x}$$

$$\left(\frac{1-2y^2\ln x}{y}\right)\frac{dy}{dx}=\frac{y^2}{x}$$ $$\begin{align}\frac{dy}{dx}&=\frac{y^3}{x(1-2y^2\ln x)}\\ &=\frac{y\cdot y^2}{x(1-2y\cdot y\ln x)}\\ \end{align}$$

$$\frac{dy}{dx}=\frac{y^2x^{y^2-1}}{1-2yx^{y^2}\ln x}$$