Derivative Calculator

Compute derivatives with step-by-step solutions.

Calculus homework can be tough, and checking your derivative answers by hand is time-consuming. Our derivative calculator computes derivatives of common functions with step-by-step solutions, so you can see exactly how the answer is derived — including the power rule, product rule, quotient rule, and chain rule in action. Students use it to verify homework, understand the steps, and prepare for exams. Just enter your function, click calculate, and get an accurate result plus a clear explanation you can learn from.

Enter a Function

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How to Use the Derivative Calculator

Our free derivative calculator computes derivatives of polynomial functions with step-by-step solutions. Enter a polynomial function using the format ax^n + bx + c (e.g., 3x^2 + 2x + 1). The calculator applies the power rule: multiply the coefficient by the power, then subtract 1 from the power, and shows each step.

Example Calculations

  • f(x) = 3x² + 2x + 1: Apply power rule to each term: d/dx[3x²] = 6x, d/dx[2x] = 2, d/dx[1] = 0. Result: f'(x) = 6x + 2.
  • f(x) = 5x³ - 4x² + 7x - 3: d/dx[5x³] = 15x², d/dx[-4x²] = -8x, d/dx[7x] = 7, d/dx[-3] = 0. Result: f'(x) = 15x² - 8x + 7.
  • f(x) = xª - 2x³ + x: d/dx[xª] = 6xª, d/dx[-2x³] = -6x², d/dx[x] = 1. Result: f'(x) = 6xª - 6x² + 1.

Frequently Asked Questions

How do I use the Derivative Calculator?
Enter a function like 3x^2 + 2x + 1 and click calculate. The calculator shows the derivative with step-by-step explanations using the power rule. Simply type your function and the result appears instantly.

What types of functions does it support?
It supports polynomial functions, including terms like ax^n, constants, and sums of terms. It also handles trigonometric functions (sin, cos, tan), exponential functions (e^x), and natural logarithms (ln).

What is the derivative of e^x?
The derivative of e^x is e^x itself. This is a unique property of the exponential function — it is the only function that is its own derivative.

How do I find the derivative of a fraction?
Use the quotient rule: (f/g)' = (f'g - fg') / g². For more complex fractions, our calculator handles this automatically by breaking down each term and applying the appropriate rule.

Does it show step-by-step solutions?
Yes, every calculation includes a step-by-step breakdown showing which derivative rule was applied to each term, making it a great learning tool for calculus students.

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