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Popular >

derivative of v(t)=t^2e^{-3t}

Solution

derivative of

v (t) = t^{2} e^{- 3 t}

Solution

2 e^{- 3 t} t - 3 e^{- 3 t} t^{2}

Solution steps

\frac{d}{d t} (t^{2} e^{- 3 t})

Apply the Product Rule:

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

f = t^{2}, g = e^{- 3 t}

= \frac{d}{d t} (t^{2}) e^{- 3 t} + \frac{d}{d t} (e^{- 3 t}) t^{2}

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

\frac{d}{d t} (e^{- 3 t}) = - 3 e^{- 3 t}

= 2 t e^{- 3 t} + (- 3 e^{- 3 t}) t^{2}

Simplify

= 2 e^{- 3 t} t - 3 e^{- 3 t} t^{2}

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Frequently Asked Questions (FAQ)

What is the derivative of v(t)=t^2e^{-3t} ?
The derivative of v(t)=t^2e^{-3t} is 2e^{-3t}t-3e^{-3t}t^2
What is the first derivative of v(t)=t^2e^{-3t} ?
The first derivative of v(t)=t^2e^{-3t} is 2e^{-3t}t-3e^{-3t}t^2