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⁄d and ᵈᵍ⁄d.

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 = x2ᵈᶠ⁄d = 3x2 and ᵈᵍ⁄d = 2x.

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

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