What is the d/(dt)((q)(-12e^{-2t})) ?

The d/(dt)((q)(-12e^{-2t})) is 24e^{-2t}q

What is the first d/(dt)((q)(-12e^{-2t})) ?

The first d/(dt)((q)(-12e^{-2t})) is 24e^{-2t}q

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\frac{d}{d t} ((q) (- 12 e^{- 2 t}))

24 e^{- 2 t} q

Solution steps

\frac{d}{d t} ((q) (- 12 e^{- 2 t}))

Treat

q

as a constant

Take the constant out:

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

= q \frac{d}{d t} (- 12 e^{- 2 t})

Take the constant out:

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

= q (- 12 \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

= q (- 12 e^{- 2 t} (- 2))

Simplify

= 24 e^{- 2 t} q

(x - 5)^{2} + (y + 6)^{2}

d (10 x^{3})

sec (3 x) (ln (5 x))

(- 4 - 4 i)^{100}

4 x^{2} + x^{2} + 4 + 25 y^{2}

What is the d/(dt)((q)(-12e^{-2t})) ?
The d/(dt)((q)(-12e^{-2t})) is 24e^{-2t}q
What is the first d/(dt)((q)(-12e^{-2t})) ?
The first d/(dt)((q)(-12e^{-2t})) is 24e^{-2t}q