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Calculus · Derivatives

Differentiate e^(-x^2)

\frac{d}{dx}\left[e^{- x^{2}}\right]

Step by step

  1. \frac{d}{dx}\left[e^{- x^{2}}\right]

    Start from the derivative to compute.

  2. e^{- x^{2}} \frac{d}{d x} \left(- x^{2}\right)

    Chain rule: (eᵘ)′ = eᵘ, times u′ where u = - x^{2}.

  3. - e^{- x^{2}} \frac{d}{d x} x^{2}

    Constant multiple rule: pull the constant out.

  4. - 2 x e^{- x^{2}}

    Power rule: (xⁿ)′ = n·xⁿ⁻¹ with n = 2.

Reveal the answer
f'(x) = - 2 x e^{- x^{2}}