If `u=f(x^3),v=g(x^2),f^(prime)(x)=cosx ,a n dg^(prime)(x)=sinx ,t h e n(d u)/(d v)` is

Options

A. `(3)/(2)x " cos "x^(3) " cosec "x^(2)`
B. `(3)/(2)" sin "x^(3) " sec "x^(2)`
C. `tan x`
D. none of these

Explanation

To solve the problem, we need to find \(\frac{du}{dv}\) given the relationships \(u = f(x^3)\) and \(v = g(x^2)\), along with the derivatives \(f'(x) = \cos x\) and \(g'(x) = \sin x\).

### Step-by-Step Solution:

1. **Identify the derivatives**:
We know that:
\[
u = f(x^3) \quad \text{and} \quad v = g(x^2)
...