Power rule for derivatives
Differentiate a polynomial using the power, constant multiple, and constant rules. Unlimited questions, five difficulty levels, and a full worked solution every time — free.
Try one
Differentiate f(x).
f(x) = −2x2 + 2x + 3
- −4x + 2
- −2x + 2
- −2x2 + 2x
- −4x - 2
Answer: -4x + 2
See one solved, step by step
Differentiate f(x).
f(x) = 5x3 + 5x + 1
- 15x2 + 5
- 5x2 + 5
- 15x2 - 5
- 5x3 + 5x
📘 Worked solution
1d/dx[5x3] = 15x2Multiply the coefficient by the exponent 3, then reduce the exponent to 2.
2d/dx[5x] = 5Same rule: multiply by 1, reduce the exponent to 0.
3d/dx[1] = 0A constant term has slope 0 everywhere, so it disappears.
4f'(x) = 15x2 + 5Add the differentiated terms together.
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