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Calculus · Derivatives

Differentiate pi·e^(-2t)/2

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

Step by step

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

    Start from the derivative to compute.

  2. \frac{\pi \frac{d}{d t} e^{- 2 t}}{2}

    Constant multiple rule: pull the constant out.

  3. \frac{\pi e^{- 2 t} \frac{d}{d t} \left(- 2 t\right)}{2}

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

  4. - \pi e^{- 2 t} \frac{d}{d t} t

    Constant multiple rule: pull the constant out.

  5. - \pi e^{- 2 t}

    d/dx of x is 1.

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