BD1 Basic Differentiation Rules - MTH 121 Spring 2026

Core Concepts¶

Power Rule¶

It’s helpful to think of this rule as a 3-step process:

Bring down the old exponent and put it in front.
Keep the variable the same.
Subtract one from the exponent.

Constant Multiple Rule¶

\dfrac{d}{dx}\bigg[ k \cdot f(x)\bigg] = k \cdot \dfrac{d}{dx}\bigg[f(x)\bigg]

This derivative tells us what to do with the derivative if we are multiplying some variable terms by a constant. We can think of this rule as telling us to move the constant-multiple out in front of the derivative process and just focus on getting the derivative of the variable terms.

Sum/Difference Rule¶

\dfrac{d}{dx}\bigg[ f(x) \pm g(x) \bigg] = \dfrac{d}{dx}\bigg[f(x)\bigg] \pm \dfrac{d}{dx}\bigg[g(x)\bigg]

We can split up the differentiation process wherever we have addition or subtraction.
This does not work for multiplication or division.

Primary Examples¶

Homework¶

Write out each question as well as your solution on the homework page template.

Make sure you leave a good amount of blank space between each question.
Write down the question as well as your solution.