Partial Derivatives Visualized | Multivariable Calculus
Partial derivatives visualized in 3 minutes: see a 3D surface sliced along x and y, the slope of each slice, and how partial derivatives power economics (marginal product) and machine learning (the gradient).▶ Full playlist: Calculus Explained Visually: https://www.youtube.com/playlist?list=PLVu1HfUDwsf8
0:00 Why one slope isn't enough
0:21 Functions of two variables as surfaces
0:45 Partial derivative with respect to x
1:09 Partial derivative with respect to y
1:25 Worked example at (1, 2)
1:46 Partial derivatives in economics
2:08 The gradient & gradient descent
2:38 Recap
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