Math Problem Statement
Kerjakan
Solution
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Math Problem Analysis
Mathematical Concepts
Derivatives
Implicit Differentiation
Velocity from Position Function
Chain Rule
Second Derivative
Formulas
f'(x) = 4x^3 - 9x^2 + 4x - 5
Implicit Differentiation: dy/dx = -x/y
Velocity: v(t) = ds/dt = 9t^2 - 12t + 9
Chain Rule: f'(x) = 7(3x^2 - 4x + 5)^6 * (6x - 4)
Second Derivative: f''(x) = -9 sin(3x)
Theorems
Power Rule for Derivatives
Implicit Differentiation
Chain Rule
Suitable Grade Level
University Level (Calculus I or II)
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