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Calculus · Derivatives

Differentiate e^(-t)·sin(x)

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

Step by step

  1. \frac{d}{dx}\left[e^{- t} \sin{\left(x \right)}\right]

    Differentiate 2 times, one derivative at a time.

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

    Constant multiple rule: pull the constant out.

  3. e^{- t} \cos{\left(x \right)}

    (sin u)′ = cos u.

  4. f^{(1)}(x) = e^{- t} \cos{\left(x \right)}

    That is derivative number 1.

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

    Constant multiple rule: pull the constant out.

  6. - e^{- t} \sin{\left(x \right)}

    (cos u)′ = −sin u.

  7. f^{(2)}(x) = - e^{- t} \sin{\left(x \right)}

    That is derivative number 2.

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