What is the derivative of t^3e^tt ?

The derivative of t^3e^tt is e^tt^4+4t^3e^t

What is the first derivative of t^3e^tt ?

The first derivative of t^3e^tt is e^tt^4+4t^3e^t

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

t^{3} e^{t} t

e^{t} t^{4} + 4 t^{3} e^{t}

Solution steps

\frac{d}{d t} (t^{3} e^{t} t)

Simplify

t^{3} e^{t} t : e^{t} t^{4}

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

Apply the Product Rule:

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

f = e^{t}, g = t^{4}

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

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

\frac{d}{d t} (t^{4}) = 4 t^{3}

= e^{t} t^{4} + 4 t^{3} e^{t}

What is the derivative of t^3e^tt ?
The derivative of t^3e^tt is e^tt^4+4t^3e^t
What is the first derivative of t^3e^tt ?
The first derivative of t^3e^tt is e^tt^4+4t^3e^t