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

The d/(dt)((x)(e^t-t)) is x(e^t-1)

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

The first d/(dt)((x)(e^t-t)) is x(e^t-1)

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

x (e^{t} - 1)

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

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

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

= x (e^{t} - 1)

(2, 5) y (- 1, - 3)

(1 - \frac{x}{3})^{11}

(x - 2 - 6) (x - 2 + 6)

5 (9 + 2)

2 x (x + 1) e^{2 x}