Concept preview

What you will be able to do

1. 01Apply the constant rule $\frac{d}{dx}c = 0$ and the constant-multiple rule $\frac{d}{dx}[cf] = cf'$ correctly.
2. 02Use the sum and difference rules to differentiate a polynomial term-by-term in a single pass.
3. 03Evaluate a polynomial derivative at a point and solve $f'(x)=0$ to locate horizontal tangents.

The constant rule says the derivative of any constant is zero: $\frac{d}{dx}\,c = 0.$ This is obvious once you picture it — the graph of $y=c$ is a horizontal line, and a horizontal line has slope $0$ everywhere. A constant does not change, so its rate of change is nothing. This is why the $+7$ at the end of a polynomial simply disappears when you differentiate.