Textbook Question
Let f(x) = x³ − 3x² − 1, x ≥ 2. Find the value of df⁻¹/dx at the point x = −1 = f(3).
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3. Techniques of Differentiation
Basic Rules of Differentiation
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Find the indicated derivative.
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Verified step by step guidance1
Identify the function to differentiate: \(-5x\).
Recognize that the derivative is with respect to \(t\), but the function is in terms of \(x\).
Since \(-5x\) is a constant with respect to \(t\), its derivative with respect to \(t\) is 0.
Apply the constant rule of differentiation: \(\frac{d}{dt}(c) = 0\) where \(c\) is a constant.
Conclude that the derivative \(\frac{d}{dt}(-5x) = 0\) because \(-5x\) does not depend on \(t\).
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