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

Options

A. 10
B. 20
C. 30
D. 40

Explanation

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

### Step 1: Define the function
Let \( f(x) = x^2 - 2 \).

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

- Differentiate \( x^2 \):
\[ \frac{d}{dx}(x^2) = 2x \]

- Differentiate the constant \(-2\):
\[ \frac{d}{dx}(-2) = 0 \]

Combining these results, we get:
\[ f'(x) = 2x + 0 = 2x \]

### Step 3: Evaluate the derivative at \( x = 10 \)
Now, we need to find \( f'(10) \):
\[ f'(10) = 2 \cdot 10 = 20 \]

### Conclusion
Thus, the derivative of \( f(x) = x^2 - 2 \) at \( x = 10 \) is \( 20 \).

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