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Polynomial Derivative Worksheet Generator

Every problem is a polynomial in x with integer coefficients. The answer key applies the power rule term by term, giving f'(x) in fully simplified polynomial form.

Polynomial Derivative Worksheet Generator

Apply the power rule to random polynomials — answers ready to mark.

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Answer10-problem worksheet — Polynomial derivatives (easy) (seed 784534583)
  1. Seed784534583 (use this seed to regenerate the same worksheet)
  2. Count10 problems
  3. Problem1. Differentiate: f(x) = 3x^2 − 2x + 3
  4. Problem2. Differentiate: f(x) = −3x^2 + x − 6
  5. Problem3. Differentiate: f(x) = 3x^2 + x + 2
  6. Problem4. Differentiate: f(x) = 4x^2 + x + 2
  7. Problem5. Differentiate: f(x) = −4x^2 − 2x + 6
  8. Problem6. Differentiate: f(x) = −4x^2 − 5x
  9. Problem7. Differentiate: f(x) = x^2 − x − 4
  10. Problem8. Differentiate: f(x) = 5x^2 + 2x − 6
  11. Problem9. Differentiate: f(x) = −3x^2 + 6x − 3
  12. Problem10. Differentiate: f(x) = −2x^2 − x − 5
  13. Answer key1. f'(x) = 6x − 2; 2. f'(x) = −6x + 1; 3. f'(x) = 6x + 1; 4. f'(x) = 8x + 1; 5. f'(x) = −8x − 2; 6. f'(x) = −8x − 5; 7. f'(x) = 2x − 1; 8. f'(x) = 10x + 2; 9. f'(x) = −6x + 6; 10. f'(x) = −4x − 1
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Frequently asked questions

What is the power rule?

d/dx (x^n) = n·x^(n−1). For a polynomial, apply it term by term and the constant disappears because d/dx (constant) = 0.

Do the polynomials include fractional exponents?

No — only non-negative integer exponents, so the practice stays focused on the power rule with whole-number powers.

What if a coefficient is negative?

Negative leading or middle coefficients appear freely. The answer key handles the signs cleanly in surd-free form.

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