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

The d/(dt)((x)(xt+x)e^t) is x(2e^tx+e^txt)

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

The first d/(dt)((x)(xt+x)e^t) is x(2e^tx+e^txt)

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

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

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the Product Rule:

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

f = x t + x, g = e^{t}

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

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

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

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

Expand

x e^{t} + e^{t} (x t + x) : 2 e^{t} x + e^{t} x t

= x (2 e^{t} x + e^{t} x t)

(e^{x} - e^{- 5 x})^{2}

\frac{1}{x ( x + b )}

e^{2 x} \cdot 2 (e^{x} + e^{- x})

\frac{( x + Δ x ) ^{3}}{Δ x}

\frac{( - 2 x + 4 ) ^{7}}{( 3 x - 5 ) ^{5}}

What is the d/(dt)((x)(xt+x)e^t) ?
The d/(dt)((x)(xt+x)e^t) is x(2e^tx+e^txt)
What is the first d/(dt)((x)(xt+x)e^t) ?
The first d/(dt)((x)(xt+x)e^t) is x(2e^tx+e^txt)