What is the d/(dt)((x)(te^t)) ?

The d/(dt)((x)(te^t)) is x(e^t+e^tt)

What is the first d/(dt)((x)(te^t)) ?

The first d/(dt)((x)(te^t)) is x(e^t+e^tt)

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

x (e^{t} + e^{t} t)

Solution steps

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

Treat

x

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

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

f = t, g = e^{t}

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

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

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

= x (1 \cdot e^{t} + e^{t} t)

Simplify

= x (e^{t} + e^{t} t)

(X + 2)^{3} + (5 X - 2)^{3}

(- x)^{3} + 2 \cdot x + 0.375

10 x^{2} - 23 + 9

\frac{2}{x ^{2} - 4}

(d x)^{2}

What is the d/(dt)((x)(te^t)) ?
The d/(dt)((x)(te^t)) is x(e^t+e^tt)
What is the first d/(dt)((x)(te^t)) ?
The first d/(dt)((x)(te^t)) is x(e^t+e^tt)