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Popular Calculus >

d/(dt)(e^tcos(t)-e^tsin(t))

Solution

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

Solution

- 2 e^{t} sin (t)

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

e^{t} cos (t) - e^{t} sin (t) - (e^{t} sin (t) + cos (t) e^{t}) : - 2 e^{t} sin (t)

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

Graph

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Frequently Asked Questions (FAQ)

What is the d/(dt)(e^tcos(t)-e^tsin(t)) ?
The d/(dt)(e^tcos(t)-e^tsin(t)) is -2e^tsin(t)
What is the first d/(dt)(e^tcos(t)-e^tsin(t)) ?
The first d/(dt)(e^tcos(t)-e^tsin(t)) is -2e^tsin(t)