This calculator uses the Power Rule to find the derivative of a single polynomial term. For any term axn, the derivative is (a × n)xn-1.
Original Function f(x):
1x2
Derivative f'(x):
2x1
The most fundamental rule for finding a derivative is the Power Rule. This rule is used when a variable is raised to a fixed power, allowing you to quickly determine the rate of change for polynomial functions.
d/dx [ax^n] = anx^(n-1)
Suppose you want to find the derivative of the function f(x) = 5x³. In this case, our coefficient 'a' is 5 and our exponent 'n' is 3.
By following these steps, the derivative of 5x³ is 15x².
What is a derivative?A derivative is a tool in calculus that measures the instantaneous rate at which a function changes at any specific point.
What is the derivative of a constant?The derivative of any constant number (like 7 or 42) is always zero because constants do not change.
Does this work for negative exponents?Yes, the power rule works for all real numbers, including negative integers and fractional exponents.
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