Multivariate Calculus and Optimization · free preview

Partial Differentiation and Gradients

Partial Differentiation and Gradients

1. Partial Differentiation and Gradients

Partial Differentiation and Gradients

2. Partial Differentiation and Gradients (2)

Partial Differentiation and Gradients (2)

3. Partial Differentiation and Gradients (3)

Partial Differentiation and Gradients (3)

4. 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

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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