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Let's say we have a function ##M(f(x))## where ##M: \mathbb{R}^2 \to \mathbb{R}^2## is a multivariable linear function, and ##f: \mathbb{R} \to \mathbb{R}^2## is a single variable function. Now I'm getting confused with evaluating the following second derivative of the function:

$$

[M(f(x))]'' = [M'(f(x)) \circ f'(x)]'

$$

How do we continue to evaluate the second derivative? This may be a very basic question, but I'm trying to get clear on the dimension of functions.

$$

[M(f(x))]'' = [M'(f(x)) \circ f'(x)]'

$$

How do we continue to evaluate the second derivative? This may be a very basic question, but I'm trying to get clear on the dimension of functions.

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