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

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

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

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

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

- e^{- t} x

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

\frac{d}{d t} (- t) = - 1

= x e^{- t} (- 1)

Simplify

= - e^{- t} x

(x - 1) (x + 1)

(r - 2)^{2} (r - 4)^{2}

e^{x} \cdot e^{1}

(- 8) \cdot (- 2)^{2} \cdot (- 2)^{0} \cdot (- 2)

\frac{( n ^{2} )}{( n + 1 ) ^{2}}

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