What is the derivative of sqrt(t)e^{-t} ?

The derivative of sqrt(t)e^{-t} is (e^{-t})/(2sqrt(t))-e^{-t}sqrt(t)

What is the first derivative of sqrt(t)e^{-t} ?

The first derivative of sqrt(t)e^{-t} is (e^{-t})/(2sqrt(t))-e^{-t}sqrt(t)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

t e^{- t}

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

\frac{d}{d t} (t) = \frac{1}{2 t}

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

= \frac{1}{2 t} e^{- t} + (- e^{- t}) t

Simplify

\frac{1}{2 t} e^{- t} + (- e^{- t}) t : \frac{e ^{- t}}{2 t} - e^{- t} t

= \frac{e ^{- t}}{2 t} - e^{- t} t

What is the derivative of sqrt(t)e^{-t} ?
The derivative of sqrt(t)e^{-t} is (e^{-t})/(2sqrt(t))-e^{-t}sqrt(t)
What is the first derivative of sqrt(t)e^{-t} ?
The first derivative of sqrt(t)e^{-t} is (e^{-t})/(2sqrt(t))-e^{-t}sqrt(t)