What is the d/(dt)(te^{5t}) ?

The d/(dt)(te^{5t}) is e^{5t}+5e^{5t}t

What is the first d/(dt)(te^{5t}) ?

The first d/(dt)(te^{5t}) is e^{5t}+5e^{5t}t

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\frac{d}{d t} (t e^{5 t})

e^{5 t} + 5 e^{5 t} t

Solution steps

\frac{d}{d t} (t e^{5 t})

Apply the Product Rule:

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

f = t, g = e^{5 t}

= \frac{d t}{d t} e^{5 t} + \frac{d}{d t} (e^{5 t}) t

\frac{d t}{d t} = 1

\frac{d}{d t} (e^{5 t}) = e^{5 t} \cdot 5

= 1 \cdot e^{5 t} + e^{5 t} \cdot 5 t

Simplify

= e^{5 t} + 5 e^{5 t} t

What is the d/(dt)(te^{5t}) ?
The d/(dt)(te^{5t}) is e^{5t}+5e^{5t}t
What is the first d/(dt)(te^{5t}) ?
The first d/(dt)(te^{5t}) is e^{5t}+5e^{5t}t