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

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

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

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

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

- e^{t} x

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

\frac{d}{d t} (2) = 0

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

= x (0 - e^{t})

Simplify

= - e^{t} x

(27 - 45) (7 + 65)

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