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Derivative of a constant function

Let $f(x) = 7$ . Find $f'(x)$ .

Hint

Recall that a constant function never changes value as $x$ changes, so think about what its rate of change must be. The constant rule states $\frac{d}{dx}[c] = 0$ for any constant $c$ .

Step-by-step solution

The function $f(x) = 7$ is a constant function — its output is always $7$ regardless of the value of $x$ . Since the graph of $f$ is a horizontal line, its slope at every point is $0$ .

By the constant rule, $\frac{d}{dx}[c] = 0$ for any constant $c$ . Applying this with $c = 7$ gives $f'(x) = 0$ .

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