What is e^{-at} d/(dt)(ye^{at}) ?

The solution to e^{-at} d/(dt)(ye^{at}) is (d/(dt)(e^{at}y))/(e^{at)}

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simplify e^{-at} d/(dt)(ye^{at})

simplify

e^{- a t} \frac{d}{d t} (y e^{a t})

\frac{\frac{d}{d t} ( e ^{a t} y )}{e ^{a t}}

Solution steps

e^{- a t} \frac{d}{d t} (y e^{a t})

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

= \frac{1}{e ^{a t}} \frac{d}{d t} (e^{a t} y)

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \frac{d}{d t} ( y e ^{a t} )}{e ^{a t}}

Multiply:

1 \frac{d}{d t} (y e^{a t}) = \frac{d}{d t} (y e^{a t})

= \frac{\frac{d}{d t} ( y e ^{a t} )}{e ^{a t}}

2.06115 \cdot 1 0^{- 9}

e^{4 x} \cdot e^{- 3 x}

g^{5} (g^{3} s^{3})

e^{- 6 ∣ t ∣}

e^{- l n (x^{\frac{a}{6}})}

What is e^{-at} d/(dt)(ye^{at}) ?
The solution to e^{-at} d/(dt)(ye^{at}) is (d/(dt)(e^{at}y))/(e^{at)}