Derivative of x Square with Respect to x Cube

Let u = x2 and v = x3.

u = x2 ----> u is a function of x

v = x3 ----> 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⁄d and ᵈⱽ⁄d.

Our aim is to find the derivative of x2 with respect to x3. 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 = x2, v = x3ᵈᵘ⁄d = 2x and ᵈⱽ⁄d = 3x2.

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

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