What is the d/(dt)(e^{-t}(asin(t)+bcos(t))) ?

The d/(dt)(e^{-t}(asin(t)+bcos(t))) is -e^{-t}(asin(t)+bcos(t))+e^{-t}(acos(t)-bsin(t))

What is the first d/(dt)(e^{-t}(asin(t)+bcos(t))) ?

The first d/(dt)(e^{-t}(asin(t)+bcos(t))) is -e^{-t}(asin(t)+bcos(t))+e^{-t}(acos(t)-bsin(t))

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

- e^{- t} (a sin (t) + b cos (t)) + e^{- t} (a cos (t) - b sin (t))

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{- t}, g = a sin (t) + b cos (t)

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

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

\frac{d}{d t} (a sin (t) + b cos (t)) = a cos (t) - b sin (t)

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

Simplify

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

\int_{0}^{6} \frac{4 t}{( t - 7 ) ^{2}} d t

e^{- 2 t} t^{2}

x \to 0 lim (x^{6} e^{- x^{5}})

\int_{1}^{\infty} x^{2} ln (x) d x

(12 y^{2} - x \cdot y) d x + (x^{2}) d y = 0

What is the d/(dt)(e^{-t}(asin(t)+bcos(t))) ?
The d/(dt)(e^{-t}(asin(t)+bcos(t))) is -e^{-t}(asin(t)+bcos(t))+e^{-t}(acos(t)-bsin(t))
What is the first d/(dt)(e^{-t}(asin(t)+bcos(t))) ?
The first d/(dt)(e^{-t}(asin(t)+bcos(t))) is -e^{-t}(asin(t)+bcos(t))+e^{-t}(acos(t)-bsin(t))