What is the d/(dt)(te^{3t}) ?

The d/(dt)(te^{3t}) is e^{3t}+3e^{3t}t

What is the first d/(dt)(te^{3t}) ?

The first d/(dt)(te^{3t}) is e^{3t}+3e^{3t}t

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

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

Solution steps

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

Apply the Product Rule:

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

f = t, g = e^{3 t}

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

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

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

= 1 \cdot e^{3 t} + e^{3 t} \cdot 3 t

Simplify

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

\frac{d}{d x} (e^{- \frac{3}{x}})

x \to 0 lim (x \cdot cot (x))

\frac{d}{d x} (x^{2} \cdot 2^{x})

2 x e^{x}

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

What is the d/(dt)(te^{3t}) ?
The d/(dt)(te^{3t}) is e^{3t}+3e^{3t}t
What is the first d/(dt)(te^{3t}) ?
The first d/(dt)(te^{3t}) is e^{3t}+3e^{3t}t