How to use: Calculate derivatives of polynomial functions (rate of change). Enter Coefficient (number in front of variable) and Power (exponent of x). Results show derivative using power rule. Formula: d/dx(ax^n) = n·a·x^(n-1). Example: For 3x⁴, enter coefficient=3, power=4 → derivative = 12x³. For 5x², enter 5 and 2 → derivative = 10x. Applications: physics velocity/acceleration (derivative of position), economics marginal cost/revenue, optimization finding maximums/minimums, engineering rate problems. Derivative represents instantaneous rate of change or slope of tangent line. Essential for calculus, physics, engineering, and mathematical modeling. Used in machine learning optimization algorithms.