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

The derivative of te^{-t} is e^{-t}-e^{-t}t

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

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

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derivative of

t e^{- t}

e^{- t} - e^{- t} t

Solution steps

\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}

= \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}

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

Simplify

= e^{- t} - e^{- t} t

\frac{d}{d x} (\frac{2 x ^{5} + 3 x ^{4} - 1}{- 2 x ^{7}})

\frac{d}{d x} (x^{3} + 2 x^{2} + x - 7)

\frac{d}{d θ} (- cos (θ))

\int \frac{6}{2 x - 5} d x

n = 0 \sum \infty \frac{0 ^{n}}{3 ^{n}}

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