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

The d/(dt)(e^{-wt}) is -e^{-wt}w

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

The first d/(dt)(e^{-wt}) is -e^{-wt}w

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

- e^{- wt} w

Solution steps

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

Treat

w

as a constant

Apply the chain rule:

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

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

\frac{d}{d t} (- wt) = - w

= e^{- wt} (- w)

Simplify

= - e^{- wt} w

e^{- 2 t} t (- t + 1)

2.00273 \cdot 1 0^{- 9} (120)

1 0^{- 9.2} \cdot 0.05

82 x^{4} y z^{4} y z

- lo g_{10} (4.7) \cdot 1 0^{- 5}