A function $y=f\left(x\right)$  satisfies $x{f}^{\text{'}}\left(x\right)-2f\left(x\right)=x^4{f}^2\left(x\right),\forall x>0$  and  $f\left(1\right)=-6$. Find the value of  $f^{\text{'}}\left(3^{\frac{1}{5}}\right)$.

Given  $\frac{xdy}{dx}-2y=x^4{y}^2$.
Now diving by  $y^2$, we get Bernouli’s differential equation.
Now after solving we get  $\frac{-2}{y}=\frac{x^4}{3}+\frac{C}{x^2}$
Now substitute the values we get  $\frac{dy}{dx}=24x^{-5}$