Calculus & Derivatives

In this lesson

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