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 `a)3/2xcosx^3cos e cx^2` `b)2/3sinx^3secx^2` `c)tanx` (d) none of these

Options

A. `(3)/(2)x " cos "x^(2) " 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 functions \(u = f(x^3)\) and \(v = g(x^2)\), where \(f'(x) = \cos x\) and \(g'(x) = \sin x\).

### Step-by-step Solution:

1. **Identify the functions:**
- \(u = f(x^3)\)
- \(v = g(x^2)\)

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