Find the derivative of `x^(2)-2` at x=10.

Explanation

To find the derivative of the function \( f(x) = x^2 - 2 \) at \( x = 10 \), we can follow these steps:

### Step 1: Define the function
We start with the function:
\[ f(x) = x^2 - 2 \]

### Step 2: Use the definition of the derivative
The derivative of a function at a point \( a \) is defined as:
\[ f'(a) = \lim_{x \to a} \frac{f(x) - f(a)}{x - a} \]
In our case, we want to find \( f'(10) \):
\[ f'(10) = \lim_{x \to 10} \frac{f(x) - f(10)}{x - 10} \]

### Step 3: Calculate \( f(10) \)
First, we need to find \( f(10) \):
\[ f(10) = 10^2 - 2 = 100 - 2 = 98 \]

### Step 4: Substitute into the derivative formula
Now we substitute \( f(10) \) into the derivative formula:
\[ f'(10) = \lim_{x \to 10} \frac{f(x) - 98}{x - 10} \]
Substituting \( f(x) \):
\[ f'(10) = \lim_{x \to 10} \frac{(x^2 - 2) - 98}{x - 10} = \lim_{x \to 10} \frac{x^2 - 100}{x - 10} \]

### Step 5: Factor the numerator
We can factor the numerator using the difference of squares:
\[ x^2 - 100 = (x - 10)(x + 10) \]
So we rewrite the limit:
\[ f'(10) = \lim_{x \to 10} \frac{(x - 10)(x + 10)}{x - 10} \]

### Step 6: Cancel the common terms
We can cancel the \( (x - 10) \) terms:
\[ f'(10) = \lim_{x \to 10} (x + 10) \]

### Step 7: Evaluate the limit
Now we can directly substitute \( x = 10 \):
\[ f'(10) = 10 + 10 = 20 \]

### Conclusion
Thus, the derivative of the function \( f(x) = x^2 - 2 \) at \( x = 10 \) is:
\[ \boxed{20} \]