Education
Derivative Calculator
Type a polynomial in x and we'll differentiate it term by term using the power rule, with a clear breakdown of each step. Polynomials only — no trig or exponentials.
Polynomials in x only — terms like 3x^2, -2x, and 5. No functions like sin or log.
Optional — leave blank or enter any real number.
Term-by-term steps
- d/dx[3x^2] = 6x · (×2, exp − 1)
- d/dx[2x] = 2 · (×1, exp − 1)
- d/dx[1] = 0 (constant)
f′(x) =
6x +2
Power rule applied term by term
Polynomial derivatives only — power rule, term by term. For chain, product, quotient, or trig/log/exp derivatives, use a full CAS like Wolfram Alpha.
Examples
f(x) = 3x² + 2x + 1
f′(x) = 6x + 2
f(x) = x³
f′(x) = 3x²
f(x) = 5x⁴ − 2x² + 7
f′(x) = 20x³ − 4x
f(x) = 4x
f′(x) = 4
How it works
Every polynomial term has the form c·xⁿ. The power rule says its derivative is the coefficient times the exponent, with the exponent dropped by one.
power rule · d/dx[c·xⁿ] = c·n·x^(n−1)
We apply this to each term and add the results. Constants (terms with no x) drop out because their derivative is zero.
Supported: polynomials in x · ^ for exponents · constants · negative coefficients. Unsupported: sin, cos, ln, e^x, products, quotients, chain rule.
Polynomials only. For trig, exponential, logarithmic, or composite functions, use a full computer-algebra system. We deliberately keep the scope narrow so every step is auditable.
Frequently asked questions
Polynomials in x only — terms like 3x^2, -2x, and constants. The calculator does not handle trig, exponential, logarithmic, product/quotient, chain rule, or implicit differentiation. For anything beyond polynomial differentiation, use a full computer algebra system like Wolfram Alpha or SymPy.
For any term c·xⁿ, the derivative is c·n·x^(n−1). Multiply the coefficient by the exponent, then drop the exponent by one. Constants (terms with no x) differentiate to 0. We apply this rule to each term in your polynomial and sum the results.
Use ^ for exponents. Spaces are optional. Examples: 3x^2 + 2x + 1, x^3 - 4x, 5, -2x + 7, 0.5x^2. The variable is always x. You can use unicode minus (−) or ASCII minus (-).
Building a safe symbolic differentiation engine for those functions would require a real computer-algebra parser. We've intentionally kept the scope to polynomials so the math stays auditable and the formula reads as exactly the power rule. If you need a CAS, Wolfram Alpha and SymPy both handle the full toolkit.
Related calculators
Education
Final Grade Calculator
Calculate your final course grade from your current grade and your final exam score.
Education
Weighted Grade Calculator
Combine assignments, quizzes, and exams by weight to get a precise weighted course average.
Education
Final Exam Calculator
Find out exactly what you need to score on your final exam to hit your target course grade.