Question

Derivative of x2 w.r.t x3 is _____________.

Answer 1

Answer: 2/3x

Step-by-step explanation:

let a = x^2 and b = x^3

differentiate a and b w.r.t x

i.e.   da/dx = 2x

       db/dx = 3x^2

now...

  da/dx  /   db/dx = da/db = 2x/3x^2 = 2/3x

Answer 2

Given:

x² w.r.t  x³

To Find:

Its derivative.

Solution:

Let a = x² and b = x³

According to the question,

On differentiating a and b w.r.t x, we get

da / dx = 2x

db / dx = 3x²

Now, in order to find derivative of x² w.r.t  x³,

 da/dx / db/dx = da / db = 2x/3x² = 2/3x

Hence, the derivative of x² w.r.t  x³ is 2/3x.