What is the d/(dt)((x)(5e^{2t})) ?

The d/(dt)((x)(5e^{2t})) is 10e^{2t}x

What is the first d/(dt)((x)(5e^{2t})) ?

The first d/(dt)((x)(5e^{2t})) is 10e^{2t}x

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\frac{d}{d t} ((x) (5 e^{2 t}))

10 e^{2 t} x

Solution steps

\frac{d}{d t} ((x) (5 e^{2 t}))

Treat

x

as a constant

Take the constant out:

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

= x \cdot 5 \frac{d}{d t} (e^{2 t})

Apply the chain rule:

e^{2 t} \frac{d}{d t} (2 t)

= e^{2 t} \frac{d}{d t} (2 t)

\frac{d}{d t} (2 t) = 2

= x \cdot 5 e^{2 t} \cdot 2

Simplify

= 10 e^{2 t} x

e^{x} (10 + 4 x) - 4 e^{x}

64 - 48 x^{2} + 12 x^{4} - x^{6}

(x + a)^{3} - (x - a)^{3}

(x + 2) (x + 3) - 4 (x + 4)

ab c + ab c

What is the d/(dt)((x)(5e^{2t})) ?
The d/(dt)((x)(5e^{2t})) is 10e^{2t}x
What is the first d/(dt)((x)(5e^{2t})) ?
The first d/(dt)((x)(5e^{2t})) is 10e^{2t}x