How to use the chain rule to find the derivatives of some exponential functions based on e? For example, how to use the chain rule to solve the derivatives of e ^ (- x ^ 2)?

Outer function: y = e ^ u
Internal function: u = φ (x)
Composite function: y = e ^ (φ (x))
Derivative: y '= [e ^ (φ (x))]' = [e ^ u] '* φ' (x) = y * φ '(x) = e ^ (φ (x)) * φ' (x)
[e^(-x^2)]'=e^(-x^2)*(-2x)

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