How to differentiate polynomials
Use this page as a straightforward polynomial differentiation guide before testing your own expression in the app.
What this topic means and what to look for first.
Polynomial differentiation is usually a power-rule question.
Differentiate each term separately, then simplify the result.
One reliable route through the topic.
- 1Write the polynomial clearly term by term.
- 2Apply the power rule to each x term.
- 3Differentiate constants to 0.
- 4Combine the derivative terms into a final simplified expression.
See the method in action.
Differentiate 5x^4 - 3x^2 + 7
- The derivative of 5x^4 is 20x^3.
- The derivative of -3x^2 is -6x.
- The derivative of 7 is 0, so the result is 20x^3 - 6x.
Differentiate x^5 + 4x
- The derivative of x^5 is 5x^4.
- The derivative of 4x is 4.
- So the derivative is 5x^4 + 4.
Things that commonly send the method off track.
- Reducing the power without multiplying by the original power first.
- Treating constants as if they still contribute a term after differentiation.
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Extra calculus revision resources
If you want more derivative and method practice after this page, these broader searches are a sensible place to continue.
Amazon
Calculus revision workbook search
Useful for more differentiation and worked-example practice in one printed workbook.
View Calculus revision workbook searchAmazon
Differentiation practice book search
Helpful if you want a narrower printed resource focused on derivative methods and routine practice.
View Differentiation practice book searchFound this useful?
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Short answers worth checking.
They differentiate to 0, so they disappear from the final derivative.
Yes. For a polynomial, term-by-term differentiation is exactly the right approach.
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