CalculusAdditional / Further Maths

Differentiating polynomials

Differentiate a polynomial term by term.

  • Apply the power rule to each term separately.
  • The derivative of is . The derivative of a constant is .
  • Keep each sign when combining the differentiated terms.

Example 1

Differentiate with respect to .

Differentiate each term; the constant gives zero.

Example 2

Differentiate with respect to .

Differentiate each term; the constant gives zero.

Your turn

Question 1

Differentiate with respect to .

Check answer
Differentiate each term; the constant gives zero.
Question 2

Differentiate with respect to .

Check answer
Differentiate each term; the constant gives zero.
Question 3

Differentiate with respect to .

Check answer
Differentiate each term; the constant gives zero.
Question 4

Differentiate with respect to .

Check answer
Differentiate each term; the constant gives zero.
Question 5

Differentiate with respect to .

Check answer
Differentiate each term; the constant gives zero.
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