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

The derivative of e^{-st} is -e^{-st}t

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

The first derivative of e^{-st} is -e^{-st}t

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derivative of

e^{- s t}

- e^{- s t} t

Solution steps

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

Treat

t

as a constant

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

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

Simplify

= - e^{- s t} t

\int sin (3 x) cos (6 x) d x

\int_{1}^{2} e^{x} d x

\int x e^{- a x} d x

\frac{1}{( 1 + s ^{2} ) ( s ^{2} + 3 )}

\int_{0}^{1} ∣ x ∣ d x

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