What is the derivative of 3e^tcos(t)-3e^tsin(t) ?

The derivative of 3e^tcos(t)-3e^tsin(t) is -6e^tsin(t)

What is the first derivative of 3e^tcos(t)-3e^tsin(t) ?

The first derivative of 3e^tcos(t)-3e^tsin(t) is -6e^tsin(t)

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derivative of

3 e^{t} cos (t) - 3 e^{t} sin (t)

- 6 e^{t} sin (t)

Solution steps

\frac{d}{d t} (3 e^{t} cos (t) - 3 e^{t} sin (t))

Apply the Sum/Difference Rule:

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

= \frac{d}{d t} (3 e^{t} cos (t)) - \frac{d}{d t} (3 e^{t} sin (t))

\frac{d}{d t} (3 e^{t} cos (t)) = 3 (e^{t} cos (t) - e^{t} sin (t))

\frac{d}{d t} (3 e^{t} sin (t)) = 3 (e^{t} sin (t) + cos (t) e^{t})

= 3 (e^{t} cos (t) - e^{t} sin (t)) - 3 (e^{t} sin (t) + cos (t) e^{t})

Simplify

3 (e^{t} cos (t) - e^{t} sin (t)) - 3 (e^{t} sin (t) + cos (t) e^{t}) : - 6 e^{t} sin (t)

= - 6 e^{t} sin (t)

f (x) = 5 x - 6 x^{2}

f (x) = e^{π} + π^{x}

\frac{d}{d x} (x^{2} - 4 x y + y^{2}) = 4

\int \frac{3 + z}{1 - z ^{2}} d z

n = 0 \sum \infty \frac{1}{n ^{2}} x^{n}

What is the derivative of 3e^tcos(t)-3e^tsin(t) ?
The derivative of 3e^tcos(t)-3e^tsin(t) is -6e^tsin(t)
What is the first derivative of 3e^tcos(t)-3e^tsin(t) ?
The first derivative of 3e^tcos(t)-3e^tsin(t) is -6e^tsin(t)