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Calculus · Derivatives

Differentiate e^(-k^2t)

\frac{d}{dt}\left[e^{- k^{2} t}\right]

Step by step

  1. \frac{d}{dt}\left[e^{- k^{2} t}\right]

    Start from the derivative to compute.

  2. e^{- k^{2} t} \frac{\partial}{\partial t} \left(- k^{2} t\right)

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

  3. - k^{2} e^{- k^{2} t} \frac{d}{d t} t

    Constant multiple rule: pull the constant out.

  4. - k^{2} e^{- k^{2} t}

    d/dx of x is 1.

Reveal the answer
f'(t) = - k^{2} e^{- k^{2} t}