What is the derivative of e^{-st}dt ?

The derivative of e^{-st}dt is -e^{-st}tdt

What is the first derivative of e^{-st}dt ?

The first derivative of e^{-st}dt is -e^{-st}tdt

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derivative of

e^{- s t} d t

- e^{- s t} t d t

Solution steps

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

Treat

t

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

= d t e^{- s t} (- t)

Simplify

= - e^{- s t} t d t

What is the derivative of e^{-st}dt ?
The derivative of e^{-st}dt is -e^{-st}tdt
What is the first derivative of e^{-st}dt ?
The first derivative of e^{-st}dt is -e^{-st}tdt