MODULE 01 · LESSON 02
Derivatives
A derivative tells how fast an output changes near one input value.
PLAIN-LANGUAGE INTRODUCTION
What is this?
A derivative tells how fast an output changes near one input value.
One simple example
Use h(t) = t² at t = 3. Its derivative there is 6.
What goes in?
A function and one point. Here, use h(t) = t² and t = 3.
What comes out?
A local slope. Here, the slope is 6.
Why does it matter?
Training needs local slopes to choose small parameter changes.
What is it not?
A derivative is not the function value. Here, the value is 9.
WORK THROUGH THE IDEA
See the idea in more detail
- A slope compares an output change with an input change. A derivative is the slope at one point.
- For
h(t) = t², the derivative ish′(t) = 2t. The mark′means derivative. - At
t = 3, compute2 × 3 = 6. This is the local slope. - A move from
3to3.1predicts a rise near6 × 0.1 = 0.6. The actual rise is9.61 − 9 = 0.61. - Common mistake: the slope
6is not the height. The height att = 3is9.