For each of the following functions, evaluate the derivative at the indicated value (s) :
`f(x)=x^(2)-2, x=10`

Answer

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

### Step 1: Find the derivative of the function
The function given is:
\[ f(x) = x^2 - 2 \]
To find the derivative \( f'(x) \), we will use the power rule of differentiation. The power rule states that if \( f(x) = x^n \), then \( f'(x) = n \cdot x^{n-1} \).

Applying the power rule to \( f(x) \):
\[ f'(x) = 2 \cdot x^{2-1} + 0 = 2x \]
(Note: The derivative of a constant, in this case, \(-2\), is \(0\).)

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

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

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