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

The derivative of e^{-t/2}-(e^{-t/2}t)/2 is (e^{-t/2}t)/4-e^{-t/2}

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

The first derivative of e^{-t/2}-(e^{-t/2}t)/2 is (e^{-t/2}t)/4-e^{-t/2}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

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

\frac{e ^{- \frac{t}{2}} t}{4} - e^{- \frac{t}{2}}

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

Simplify

- \frac{1}{2} e^{- \frac{t}{2}} - \frac{1}{2} (- \frac{e ^{- \frac{t}{2}} t}{2} + e^{- \frac{t}{2}}) : \frac{e ^{- \frac{t}{2}} t}{4} - e^{- \frac{t}{2}}

= \frac{e ^{- \frac{t}{2}} t}{4} - e^{- \frac{t}{2}}

y = 8 x - 6, (64, 58)

\int_{7}^{9} (x^{2} + 2 x - 5) d x

\int x^{2} e^{4 x} d x

\frac{1}{s ^{2} + 6 s + 25}

f (x) = \frac{7 x}{e ^{x}}

What is the derivative of e^{-t/2}-(e^{-t/2}t)/2 ?
The derivative of e^{-t/2}-(e^{-t/2}t)/2 is (e^{-t/2}t)/4-e^{-t/2}
What is the first derivative of e^{-t/2}-(e^{-t/2}t)/2 ?
The first derivative of e^{-t/2}-(e^{-t/2}t)/2 is (e^{-t/2}t)/4-e^{-t/2}