What is the d/(dt)((q)(0.01-0.01e^{-50t})) ?

The d/(dt)((q)(0.01-0.01e^{-50t})) is 0.5e^{-50t}q

What is the first d/(dt)((q)(0.01-0.01e^{-50t})) ?

The first d/(dt)((q)(0.01-0.01e^{-50t})) is 0.5e^{-50t}q

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\frac{d}{d t} ((q) (0.01 - 0.01 e^{- 50 t}))

0.5 e^{- 50 t} q

Solution steps

\frac{d}{d t} ((q) (0.01 - 0.01 e^{- 50 t}))

Treat

q

as a constant

Take the constant out:

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

= q \frac{d}{d t} (0.01 - 0.01 e^{- 50 t})

Apply the Sum/Difference Rule:

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

= q (\frac{d}{d t} (0.01) - \frac{d}{d t} (0.01 e^{- 50 t}))

\frac{d}{d t} (0.01) = 0

\frac{d}{d t} (0.01 e^{- 50 t}) = - 0.5 e^{- 50 t}

= q (0 - (- 0.5 e^{- 50 t}))

Simplify

= 0.5 e^{- 50 t} q

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(1 - e^{- 4 s})^{3}

(18 + \frac{5}{4 ln ( 2 )}) 2

3 (\frac{2}{3} m - 6 n)

What is the d/(dt)((q)(0.01-0.01e^{-50t})) ?
The d/(dt)((q)(0.01-0.01e^{-50t})) is 0.5e^{-50t}q
What is the first d/(dt)((q)(0.01-0.01e^{-50t})) ?
The first d/(dt)((q)(0.01-0.01e^{-50t})) is 0.5e^{-50t}q