A function `f,` defined for all positive real numbers, satisfies the equation `f(x^2)=x^3` for every `x >0` . Then the value of `f^(prime)(4)` is 12 (b) 3 (c) `3//2` (d) cannot be determined

Options

A. 12
B. 3
C. `3//2`
D. cannot be determined

Explanation

To solve the problem step by step, we start with the given function and its properties.

### Step 1: Understand the given function
We have a function \( f \) defined for all positive real numbers such that:
\[ f(x^2) = x^3 \quad \text{for every } x > 0 \]

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