Constant and Sum Rules
Derivative of constant is 0; derivatives add.
Key idea
Derivative of constant is 0; derivatives add.
In depth
The derivative of a constant is 0, (cf)′ = cf′, and (f + g)′ = f′ + g′. Differentiation is linear, so you can differentiate term by term.
Worked example
d/dx (4x³ − 5x + 7) = 12x² − 5.
Real-world uses
- Differentiating multi-part cost formulas such as fixed fee plus variable charges
Common mistake
Differentiating a constant multiple by differentiating the constant too.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Constant and Sum Rules?
Derivative of constant is 0; derivatives add. It is a topic at the advanced level in Calculus.
Where is Constant and Sum Rules used in real life?
Real-world examples: Differentiating multi-part cost formulas such as fixed fee plus variable charges.
What should I learn before Constant and Sum Rules?
Make sure you are comfortable with Power Rule, the previous topic in Calculus.
What is a common mistake with Constant and Sum Rules?
Differentiating a constant multiple by differentiating the constant too.
How can I practise Constant and Sum Rules?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Constant and Sum Rules?
Move on to Product Rule next.
Related advanced topics in Calculus
- Idea of a Limit – The value a function approaches as the input approaches a point.
- One-Sided Limits – Left and right limits must agree for the limit to exist.
- Limit Laws – Limits of sums, products and quotients are computed from the parts.
- Factoring and Rationalizing Limits – Remove 0/0 indeterminacy with algebra.
- Limits at Infinity – End behaviour of functions.
- Infinite Limits and Asymptotes – Function values grow without bound near a vertical asymptote.