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Popular >

d/(dt)(-e^{-4t}+4te^{-4t})

Solution

\frac{d}{d t} (- e^{- 4 t} + 4 t e^{- 4 t})

Solution

8 e^{- 4 t} - 16 e^{- 4 t} t

Solution steps

\frac{d}{d t} (- e^{- 4 t} + 4 t e^{- 4 t})

Apply the Sum/Difference Rule:

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

= - \frac{d}{d t} (e^{- 4 t}) + \frac{d}{d t} (4 t e^{- 4 t})

\frac{d}{d t} (e^{- 4 t}) = - 4 e^{- 4 t}

\frac{d}{d t} (4 t e^{- 4 t}) = 4 (e^{- 4 t} - 4 e^{- 4 t} t)

= - (- 4 e^{- 4 t}) + 4 (e^{- 4 t} - 4 e^{- 4 t} t)

Simplify

- (- 4 e^{- 4 t}) + 4 (e^{- 4 t} - 4 e^{- 4 t} t) : 8 e^{- 4 t} - 16 e^{- 4 t} t

= 8 e^{- 4 t} - 16 e^{- 4 t} t

Graph

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Frequently Asked Questions (FAQ)

What is the d/(dt)(-e^{-4t}+4te^{-4t}) ?
The d/(dt)(-e^{-4t}+4te^{-4t}) is 8e^{-4t}-16e^{-4t}t
What is the first d/(dt)(-e^{-4t}+4te^{-4t}) ?
The first d/(dt)(-e^{-4t}+4te^{-4t}) is 8e^{-4t}-16e^{-4t}t