Three Forms, One Sign Rule

You'll learnwhere the six inverse trig derivatives come from, why three of them carry a minus, and how to tell by the shape of a graph that you have not swapped two of them.

Arcsine stands up vertically at both ends. Arctangent flattens out forever. Their derivatives have to look as different as that, and once you can see it you cannot mix them up. Twelve short steps; press Next for each one.

12 STEPS · 6 QUICK CHECKS · THREE FORMS + ONE SIGN RULE · READ THE SHAPE · v2

three families · each co-function is its partner, negated

Before you start

What you're looking at

The graph of arcsine, which exists only between −1 and 1. Every slope you will see is measured off the plotted curve.

The question

Why does arcsine get a radical and arctangent get a sum, and how do you tell you have not swapped them?

Step 1 / 12