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Calculus · Derivatives

Differentiate e^(-2t)·sin(x)·cos(y)

\frac{d}{dt}\left[e^{- 2 t} \sin{\left(x \right)} \cos{\left(y \right)}\right]

Step by step

  1. \frac{d}{dt}\left[e^{- 2 t} \sin{\left(x \right)} \cos{\left(y \right)}\right]

    Start from the derivative to compute.

  2. \sin{\left(x \right)} \cos{\left(y \right)} \frac{d}{d t} e^{- 2 t}

    Constant multiple rule: pull the constant out.

  3. e^{- 2 t} \sin{\left(x \right)} \cos{\left(y \right)} \frac{d}{d t} \left(- 2 t\right)

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

  4. - 2 e^{- 2 t} \sin{\left(x \right)} \cos{\left(y \right)} \frac{d}{d t} t

    Constant multiple rule: pull the constant out.

  5. - 2 e^{- 2 t} \sin{\left(x \right)} \cos{\left(y \right)}

    d/dx of x is 1.

Reveal the answer
f'(t) = - 2 e^{- 2 t} \sin{\left(x \right)} \cos{\left(y \right)}