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))

\int \frac{3 x + 7}{3 x + 8} d x

y^{^{'}} = \frac{( 6 x ^{3} + y ^{3} )}{x y ^{2}}

y^{^{'}} = 1 - 100 (y - t)

\int_{0}^{\infty} \frac{1}{x ^{2}} d x

\int \frac{2 x + 1}{( x ^{2} + 6 x + 10 ) ( x + 1 )} d x

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))