Derivative of x Cube with Respect to x Square

Let f = x³ and g = x².

f = x³ ----> f is a function of x

g = x² ----> 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 x² with respect to x³. 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 = x³, g = x², ᵈᶠ⁄dₓ = 3x² and ᵈᵍ⁄dₓ = 2x.

Derivative of x³ with respect to x² is ²⁄₃ₓ.

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