Multivariate Calculus and Optimization · 免费预览

偏导数与梯度

偏导数与梯度

1. Partial Differentiation and Gradients

Partial Differentiation and Gradients

2. Quick check: Partial derivative

Computing ∂f/∂x1\partial f / \partial x_1 of f(x1,x2)=x12x2f(x_1, x_2) = x_1^2 x_2 treats x2x_2 as

3. Partial Differentiation and Gradients (2)

Partial Differentiation and Gradients (2)

4. Partial Differentiation and Gradients (3)

Partial Differentiation and Gradients (3)

5. Gradient of a linear function

For f(x)=a⊤xf(x) = a^\top x with fixed aa, the gradient ∇f(x)\nabla f(x) is ______ .

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