Help with step $3$ please

Tutorial Exercise

Use logarithmic differentiation to find $d\frac{y}{d}x.$

$y=x^{\frac{5}{x}},x>0$

Step $1$

To find the derivative of the function $y=x^{\frac{5}{x}},$ apply the natural logarithmic function to each side of the equation. Therefore,

In

$In$

$(y)=lnln(x^{\frac{5}{x}})$

$=\frac{5}{x}ln(x).$

Step $2$

Differentiate $ln(y)=\frac{5}{x}ln(x)$ with respect to $x.$

$\{\begin{array}{c}\text{:}\frac{d}{dx}(ln(y))=\frac{d}{dx}(\frac{5}{x}ln(x))\end{array}$

Step $3$

Solve $\frac{1}{y}(\frac{dy}{dx})=\frac{5}{x^2}(1-ln(x))$ for $\frac{dy}{dx}.$

$\frac{dy}{dx}=\frac{5y}{x^2}(1-ln(x))$

Substitute $y=x^{\frac{5}{x}}$ in $\frac{dy}{dx}=\frac{5y}{x^2}(1-ln(x)).$ Therefore,