What is the derivative of 0.0225te^{-0.0467t} ?

The derivative of 0.0225te^{-0.0467t} is 0.0225(e^{-0.0467t}-0.0467e^{-0.0467t}t)

What is the first derivative of 0.0225te^{-0.0467t} ?

The first derivative of 0.0225te^{-0.0467t} is 0.0225(e^{-0.0467t}-0.0467e^{-0.0467t}t)

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derivative of

0.0225 t e^{- 0.0467 t}

0.0225 (e^{- 0.0467 t} - 0.0467 e^{- 0.0467 t} t)

Solution steps

\frac{d}{d t} (0.0225 t e^{- 0.0467 t})

Take the constant out:

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

= 0.0225 \frac{d}{d t} (t e^{- 0.0467 t})

Apply the Product Rule:

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

f = t, g = e^{- 0.0467 t}

= 0.0225 (\frac{d t}{d t} e^{- 0.0467 t} + \frac{d}{d t} (e^{- 0.0467 t}) t)

\frac{d t}{d t} = 1

\frac{d}{d t} (e^{- 0.0467 t}) = - 0.0467 e^{- 0.0467 t}

= 0.0225 (1 \cdot e^{- 0.0467 t} + (- 0.0467 e^{- 0.0467 t}) t)

Simplify

= 0.0225 (e^{- 0.0467 t} - 0.0467 e^{- 0.0467 t} t)

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What is the derivative of 0.0225te^{-0.0467t} ?
The derivative of 0.0225te^{-0.0467t} is 0.0225(e^{-0.0467t}-0.0467e^{-0.0467t}t)
What is the first derivative of 0.0225te^{-0.0467t} ?
The first derivative of 0.0225te^{-0.0467t} is 0.0225(e^{-0.0467t}-0.0467e^{-0.0467t}t)