Let u = x^{2} and v = x^{3}.
u = x^{2} > u is a function of x
v = x^{3} > v is a function of x
Since both u and v are the functions of x, we can find the derivatives of u and v with resepct to x.
That is, ᵈᵘ⁄dₓ and ᵈⱽ⁄dₓ.


Our aim is to find the derivative of x^{2} with respect to x^{3}. That is, derivative of u with respect to v.
When both u and v are the functions of x, formula to find the derivative of u with respect to v :
Substitute u = x^{2}, v = x^{3}, ᵈᵘ⁄dₓ = 2x and ᵈⱽ⁄dₓ = 3x^{2}.
Derivative of x^{2} with respect to x^{3} is ²⁄₃ₓ.
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