Find the derivative of `f(x) = 10x `at` x=10`.

Answer

To find the derivative of the function \( f(x) = 10x \) at \( x = 10 \), we can follow these steps:

### Step 1: Identify the function
We have the function:
\[ f(x) = 10x \]

### Step 2: Find the derivative
To find the derivative \( f'(x) \), we apply the power rule of differentiation. The power rule states that if \( f(x) = ax^n \), then \( f'(x) = n \cdot ax^{n-1} \).

In our case:
- \( a = 10 \)
- \( n = 1 \)

Using the power rule:
\[ f'(x) = 1 \cdot 10x^{1-1} = 10x^0 = 10 \cdot 1 = 10 \]

### Step 3: Evaluate the derivative at \( x = 10 \)
Since the derivative \( f'(x) = 10 \) is a constant, it does not depend on \( x \). Therefore, at \( x = 10 \):
\[ f'(10) = 10 \]

### Final Answer
The derivative of \( f(x) = 10x \) at \( x = 10 \) is:
\[ \boxed{10} \]

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