What is the derivative of 6te^{-t} ?

The derivative of 6te^{-t} is 6(e^{-t}-e^{-t}t)

What is the first derivative of 6te^{-t} ?

The first derivative of 6te^{-t} is 6(e^{-t}-e^{-t}t)

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derivative of

6 t e^{- t}

6 (e^{- t} - e^{- t} t)

Solution steps

\frac{d}{d t} (6 t e^{- t})

Take the constant out:

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

= 6 \frac{d}{d t} (t e^{- t})

Apply the Product Rule:

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

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

= 6 (\frac{d t}{d t} e^{- t} + \frac{d}{d t} (e^{- t}) t)

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

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

= 6 (1 \cdot e^{- t} + (- e^{- t}) t)

Simplify

= 6 (e^{- t} - e^{- t} t)

What is the derivative of 6te^{-t} ?
The derivative of 6te^{-t} is 6(e^{-t}-e^{-t}t)
What is the first derivative of 6te^{-t} ?
The first derivative of 6te^{-t} is 6(e^{-t}-e^{-t}t)