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Popular >

d/(dt)(-e^{-t}sin(t)+e^{-t}cos(t))

Solution

\frac{d}{d t} (- e^{- t} sin (t) + e^{- t} cos (t))

Solution

- 2 e^{- t} cos (t)

Solution steps

\frac{d}{d t} (- e^{- t} sin (t) + e^{- t} cos (t))

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= - \frac{d}{d t} (e^{- t} sin (t)) + \frac{d}{d t} (e^{- t} cos (t))

\frac{d}{d t} (e^{- t} sin (t)) = - e^{- t} sin (t) + e^{- t} cos (t)

\frac{d}{d t} (e^{- t} cos (t)) = - e^{- t} cos (t) - e^{- t} sin (t)

= - (- e^{- t} sin (t) + e^{- t} cos (t)) - e^{- t} cos (t) - e^{- t} sin (t)

Simplify

= - 2 e^{- t} cos (t)

Graph

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Frequently Asked Questions (FAQ)

What is the d/(dt)(-e^{-t}sin(t)+e^{-t}cos(t)) ?
The d/(dt)(-e^{-t}sin(t)+e^{-t}cos(t)) is -2e^{-t}cos(t)
What is the first d/(dt)(-e^{-t}sin(t)+e^{-t}cos(t)) ?
The first d/(dt)(-e^{-t}sin(t)+e^{-t}cos(t)) is -2e^{-t}cos(t)