What is the d/(dt)((x)(e^{-2t})) ?

The d/(dt)((x)(e^{-2t})) is -2e^{-2t}x

What is the first d/(dt)((x)(e^{-2t})) ?

The first d/(dt)((x)(e^{-2t})) is -2e^{-2t}x

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\frac{d}{d t} ((x) (e^{- 2 t}))

- 2 e^{- 2 t} x

Solution steps

\frac{d}{d t} ((x) (e^{- 2 t}))

Treat

x

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= x \frac{d}{d t} (e^{- 2 t})

Apply the chain rule:

e^{- 2 t} \frac{d}{d t} (- 2 t)

= e^{- 2 t} \frac{d}{d t} (- 2 t)

\frac{d}{d t} (- 2 t) = - 2

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

Simplify

= - 2 e^{- 2 t} x

\frac{( ln ( \frac{1}{4} ) ) ^{2}}{π ^{2} + ( ln ( \frac{1}{4} ) ) ^{2}}

(5 3 v)^{3}

(15 a^{2} b^{3} c^{2}) (2 a b^{3} c^{5})

x - 7 \cdot x + 1

\frac{1875.3944 1 ^{2}}{1239.842} \cdot 5.79 \cdot 1 0^{- 5}

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