## 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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