Differentiate `x^2` with respect to `x^3dot`

Explanation

Let `u=x^{2}` and `v=x^{3}`



`Rightarrow frac{d u}{d x}=2 x text { and } frac{d v}{d x}=3 x^{2} `


`therefore frac{d u}{d v}=frac{frac{d u}{d x}}{frac{d v}{d x}}=frac{2 x}{3 x^{2}}=frac{2}{3 x}`