Gradients of Vector-Valued Functions

Gradients of Vector-Valued Functions

Gradients of Vector-Valued Functions (2)

Gradients of Vector-Valued Functions (3)

Gradients of Vector-Valued Functions (4)

Gradients of Vector-Valued Functions (5)

Gradients of Vector-Valued Functions (6)

Gradients of Vector-Valued Functions (7)

Gradients of Vector-Valued Functions (8)

Gradients of Vector-Valued Functions (9)

Gradients of Vector-Valued Functions (10)

Gradients of Vector-Valued Functions (11)

For $f: \mathbb{R}^n \to \mathbb{R}^m$, the Jacobian $J$ has shape

For $h(x) = g(f(x))$, the Jacobian of $h$ is