Question

Derivative of x² with respect to x³, is ______.

Options

• `2/(3x)`

• `(3x)/2`

• `(2x)/3`

• 6x⁵

Answer 1

Derivative of x² with respect to x³, is `underlinebb(2/(3x))`.

Explanation:

Let y = x²

& z = x³

then `dy/dx = 2x`   ...(i)

& `dz/dx = 3x^2`   ...(ii)

(i) ÷ (ii)

`dy/dz = (2x)/(3x^2) = 2/(3x)`

= `(d(x^2))/(d(x^3))=(dx^2/dx)/(dx^3/dx)`

= `2/(3x)`