Consider the function   , where    is a constant parameter. The first derivative of this function with respect to the variable   is

To analyze the first derivative of the given function with respect to the variable $x$ where $a$ is a constant parameter, we can outline the steps as follows:

1. Break Down the Problem

We don't have a specific function mentioned, but generally, we need to:

• Identify the function $f(x)$.
• Take its derivative with respect to $x$.

2. Relevant Concepts

We will use the basic rules of differentiation. Common derivatives include:

• Power rule: If $f(x) = x^n$, then $f'(x) = nx^{n-1}$.
• Constant multiple rule: If $f(x) = a \cdot g(x)$, then $f'(x) = a \cdot g'(x)$.
• Sum rule: If $f(x) = g(x) + h(x)$, then $f'(x) = g'(x) + h'(x)$.

3. Analysis and Detail

Assuming our function takes a form such as $f(x) = a \cdot g(x) + h(x)$:

1. Compute $g'(x)$ and $h'(x)$ based on their specific forms.
2. Combine results according to the rules stated in the relevant concepts.

4. Verify and Summarize

Make sure all steps align with the derived rules and recheck computations if necessary.

Final Answer

For a specific function $f(x)$, the first derivative $\frac{df}{dx}$ would be computed using the differentiation rules mentioned. If you provide the exact function, I can give a precise derivative.