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Popular >

d/(dt)(20(1-e^{-t/2}))

Solution

\frac{d}{d t} (20 (1 - e^{- \frac{t}{2}}))

Solution

10 e^{- \frac{t}{2}}

Solution steps

\frac{d}{d t} (20 (1 - e^{- \frac{t}{2}}))

Take the constant out:

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

= 20 \frac{d}{d t} (1 - e^{- \frac{t}{2}})

Apply the Sum/Difference Rule:

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

= 20 (\frac{d}{d t} (1) - \frac{d}{d t} (e^{- \frac{t}{2}}))

\frac{d}{d t} (1) = 0

\frac{d}{d t} (e^{- \frac{t}{2}}) = - \frac{1}{2} e^{- \frac{t}{2}}

= 20 (0 - (- \frac{1}{2} e^{- \frac{t}{2}}))

Simplify

20 (0 - (- \frac{1}{2} e^{- \frac{t}{2}})) : 10 e^{- \frac{t}{2}}

= 10 e^{- \frac{t}{2}}

Graph

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Frequently Asked Questions (FAQ)

What is the d/(dt)(20(1-e^{-t/2})) ?
The d/(dt)(20(1-e^{-t/2})) is 10e^{-t/2}
What is the first d/(dt)(20(1-e^{-t/2})) ?
The first d/(dt)(20(1-e^{-t/2})) is 10e^{-t/2}