Differentiation

In this lesson

1. 01Why derivatives run machine learningIntroduce the role of derivatives in understanding and improving machine learning models.0:00
2. 02What a derivative is measuringInterpret a derivative as the rate of change of a function and read its meaning from a curve.2:56
3. 03LimitsShrink the gap between two points toward zero to build a derivative from the limits definition.5:50
4. 04Reading the signUse the sign of the derivative to identify which direction increases or decreases a function.8:29
5. 05The rulesDerive the derivative of x squared, then apply the power, constant, and sum rules and the derivatives of log x and e to the x.10:40
6. 06The chain ruleApply the chain rule to composed functions and connect it to the idea behind backpropagation.13:52
7. 07Maxima and minimaUnderstand what maxima and minima represent on a curve and how derivatives help locate them.16:36
8. 08Actually finding oneWork through finding a candidate maximum or minimum by setting the derivative to zero and solving.17:41
9. 09Local and globalDistinguish a local minimum from a global minimum and understand why the distinction matters.20:51
10. 10When you can't solve itExplore why gradient descent is useful when the equation for a stationary point cannot be solved directly.23:01
11. 11When x is a vectorExtend derivatives to functions of several variables and interpret the components of a gradient vector.26:30

• Why derivatives run ML · what a derivative measures · letting the gap go to zero
• Reading the sign · the rules · the chain rule · maxima and minima · actually finding one
• Local and global · when you can't solve it · when x is a vector (the gradient)