What is the derivative of s(t)=4e^{-2t}sin(2pit) ?

The derivative of s(t)=4e^{-2t}sin(2pit) is 4(-2e^{-2t}sin(2pit)+2pie^{-2t}cos(2pit))

What is the first derivative of s(t)=4e^{-2t}sin(2pit) ?

The first derivative of s(t)=4e^{-2t}sin(2pit) is 4(-2e^{-2t}sin(2pit)+2pie^{-2t}cos(2pit))

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derivative of

s (t) = 4 e^{- 2 t} sin (2 π t)

4 (- 2 e^{- 2 t} sin (2 π t) + 2 π e^{- 2 t} cos (2 π t))

Solution steps

\frac{d}{d t} (4 e^{- 2 t} sin (2 π t))

Take the constant out:

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

= 4 \frac{d}{d t} (e^{- 2 t} sin (2 π t))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{- 2 t}, g = sin (2 π t)

= 4 (\frac{d}{d t} (e^{- 2 t}) sin (2 π t) + \frac{d}{d t} (sin (2 π t)) e^{- 2 t})

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

\frac{d}{d t} (sin (2 π t)) = cos (2 π t) \cdot 2 π

= 4 ((- 2 e^{- 2 t}) sin (2 π t) + cos (2 π t) \cdot 2 π e^{- 2 t})

Simplify

= 4 (- 2 e^{- 2 t} sin (2 π t) + 2 π e^{- 2 t} cos (2 π t))

What is the derivative of s(t)=4e^{-2t}sin(2pit) ?
The derivative of s(t)=4e^{-2t}sin(2pit) is 4(-2e^{-2t}sin(2pit)+2pie^{-2t}cos(2pit))
What is the first derivative of s(t)=4e^{-2t}sin(2pit) ?
The first derivative of s(t)=4e^{-2t}sin(2pit) is 4(-2e^{-2t}sin(2pit)+2pie^{-2t}cos(2pit))