Differentiation Splits a Sum, and Stops at a Product

You'll learnhow to differentiate a polynomial one term at a time, why a constant vanishes and a coefficient rides through, and where that license runs out.

Lift a whole curve by 3 and not one tangent turns. Stretch it by 2 and every tangent steepens by 2. Those two pictures are the rules that let a polynomial be differentiated one term at a time. Twelve short steps; press Next for each one.

12 STEPS · 6 QUICK CHECKS · A CONSTANT DIFFERENTIATES TO 0, NOT TO ITSELF · LINEARITY STOPS AT A PRODUCT · v2

f(x) = x³ − 3x² + 3 · f′(x) = 3x² − 6x

Before you start

What you're looking at

The curve f(x) = x³ − 3x² + 3, a polynomial with three terms.

The question

Can each term be differentiated on its own, and which parts of an expression does that license not cover?

Step 1 / 12