Calculadora de Derivadas (potências)
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
f(x) = a·xⁿ ⇒ f′(x) = a·n·xⁿ⁻¹
About this calculator
This derivative calculator solves the derivative of functions of the form f(x) = a·xⁿ at a specific point x₀. It applies the power rule, a fundamental rule of differential calculus, to provide the derivative value f′(x₀) = a·n·x₀ⁿ⁻¹. The tool is useful for students and professionals who need a quick and accurate calculation, avoiding manual errors.
The operation is simple: you enter the coefficients a and n of the function, as well as the point x₀ where you want to calculate the derivative. The calculator then automatically applies the formula: multiplies the coefficient a by the exponent n, reduces the exponent by 1, and computes the numerical result. The process is instantaneous and requires no prior calculus knowledge, just identification of the function parameters.
Use this calculator in situations such as checking differential calculus exercises, preparing for exams, or analyzing instantaneous rates of change in physical or economic models involving powers. It is ideal for simple polynomial functions where the power rule applies directly, without the need for additional rules like product or quotient.
Important precautions: ensure the function is in the form a·xⁿ, without additional terms. The calculator does not handle trigonometric, exponential, or logarithmic functions. Also, the exponent n can be any real number, but the calculator assumes the function is differentiable at x₀. For n = 0, the derivative is zero, and for n = 1, the derivative is the constant a.
Frequently asked questions
Can I use this calculator for functions with more than one term, like f(x) = 3x² + 2x?
No, this calculator handles only a single term of the form a·xⁿ. For functions with multiple terms, you should calculate the derivative of each term separately and sum the results.
What happens if I enter a negative exponent?
The calculator works normally with negative exponents. For example, for f(x) = 2·x⁻³, the derivative will be -6·x⁻⁴. Just ensure that the point x₀ is not zero, as the function may not be defined there.
Does the calculator provide the derivative at a point or the derivative function?
It provides the numerical value of the derivative at the specified point x₀. If you need the generic derivative function, you should use another tool or calculate manually.
Can I use fractional exponents, like n = 0.5?
Yes, the calculator accepts real exponents, including fractions. Remember that the function must be differentiable at the point, and for exponents between 0 and 1, the derivative may tend to infinity at x₀ = 0.
Does the calculator work for functions with coefficient a = 0?
Yes, if a = 0, the function is constant (f(x) = 0) and the derivative will be zero at any point. The calculator will return 0.