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⁄dₓ and ᵈⱽ⁄dₓ.

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 = x³, ᵈᵘ⁄dₓ = 2x and ᵈⱽ⁄dₓ = 3x².

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

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