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Home » The Punisher Cast: Hidden Moments That Made Me Cry (And Scream!) - AIKO, infinite ways to autonomy.

The Punisher Cast: Hidden Moments That Made Me Cry (And Scream!) - AIKO, infinite ways to autonomy.

📅 May 5, 2026 👤 scraface

May 05, 2026

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P(t) = \frac{1000}{D(t)} \Rightarrow P'(t) = -1000 \cdot \frac{D'(t)}{...
Now compute $ D'(t) $:
D(t) = 1 + 9e^{-0.5t} \Rightarrow D'(t) = 9 \cdot (-0.5)e^{-0.5t} = -4...
P'(t) = -1000 \cdot \frac{-4.5e^{-0.5t}}{(1 + 9e^{-0.5t})^2} = \frac{4...
To find the maximum of $ P'(t) $, we define:
f(t) = \frac{e^{-0.5t}}{(1 + 9e^{-0.5t})^2}.
Let $ u = e^{-0.5t} $, so $ f(t) = \frac{u}{(1 + 9u)^2} $. Now find th...
f(u) = \frac{u}{(1 + 9u)^2}.
Differentiate using the quotient rule:
f'(u) = \frac{(1 + 9u)^2 \cdot 1 - u \cdot 2(1 + 9u)(9)}{(1 + 9u)^4}.

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