if   f(x) = x + 5 and g(x) = x ^ 2 - 3 what  will d(f(x)) be?

To find \( d(f(x)) \), we need to compute the derivative of \( f(x) = x + 5 \).

### Solution:
1. The function \( f(x) = x + 5 \) is a simple linear function.
2. The derivative of \( f(x) \) with respect to \( x \), denoted \( f'(x) \) or \( d(f(x)) \), is obtained by differentiating each term:
   \[
   f'(x) = \frac{d}{dx}(x) + \frac{d}{dx}(5)
   \]
3. Since the derivative of \( x \) is \( 1 \) and the derivative of a constant \( 5 \) is \( 0 \), we get:
   \[
   f'(x) = 1
   \]

So, \( d(f(x)) = 1 \).

Would you like details on differentiating \( g(x) \) as well, or have any other questions?

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Here are some related questions that explore similar ideas:

1. What is the derivative of \( g(x) = x^2 - 3 \)?
2. How would you find the derivative of a product of \( f(x) \) and \( g(x) \)?
3. What is the second derivative of \( f(x) = x + 5 \)?
4. How do you find the derivative of a composite function like \( h(x) = f(g(x)) \)?
5. If \( f(x) = x + 5 \) and \( g(x) = x^2 - 3 \), what is \( f'(g(x)) \)?

**Tip:** The derivative of a constant is always zero, simplifying calculations for functions involving constants.

If f(x) = x + 5 and g(x) = x^2 - 3, what will d(f(x)) be?

Explore the step-by-step solution to find the derivative of the function f(x) = x + 5. This problem demonstrates essential calculus concepts, including the power rule and constant rule, ideal for Grades 11-12.

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