Let f = x^{3} and g = x^{2}.
f = x^{3} > f is a function of x
g = x^{2} > g is a function of x
Since both f and g are the functions of x, we can find the derivatives of f and g with resepct to x.
That is, ᵈᶠ⁄dₓ and ᵈᵍ⁄dₓ.


Our aim is to find the derivative of x^{2} with respect to x^{3}. That is, derivative of f with respect to g.
When both f and g are the functions of x, formula to find the derivative of f with respect to g :
Substitute f = x^{3}, g = x^{2}, ᵈᶠ⁄dₓ = 3x^{2} and ᵈᵍ⁄dₓ = 2x.
Derivative of x^{3} with respect to x^{2} is ²⁄₃ₓ.
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