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Home » Rearrange to isolate terms with \( x \): - Silent Sales Machine

Rearrange to isolate terms with \( x \): - Silent Sales Machine

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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I''(t) = rac{N'(t)D(t) - N(t)D'(t)}{[D(t)]^2}.
Compute derivatives:
N'(t) = 2 - 4t^3, \quad D'(t) = 2(1 + t^3)(3t^2) = 6t^2(1 + t^3).
I''(t) = rac{(2 - 4t^3)(1 + t^3)^2 - (2t - t^4)(6t^2(1 + t^3))}{(1 +...
Factor \( (1 + t^3) \) from numerator:
I''(t) = rac{(1 + t^3)\left[(2 - 4t^3)(1 + t^3) - 6t^2(2t - t^4)
ight]}{(1 + t^3)^4} = rac{(2 - 4t^3)(1 + t^3) - 6t^2(2t - t^4)}{(1 +...
First term:
Second term:
-6t^2(2t - t^4) = -12t^3 + 6t^6.

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