CalculusAdditional / Further Maths

Differentiating negative powers

Rewrite reciprocal powers and differentiate them.

  • Rewrite as .
  • Use the same power rule: .
  • The original function and derivative require .

Example 1

Differentiate with respect to . Work on .

Rewrite the reciprocal as a negative power.Apply the power rule.

Example 2

Differentiate with respect to . Work on .

Rewrite the reciprocal as a negative power.Apply the power rule.

Your turn

Question 1

Differentiate with respect to . Work on .

Check answer
Rewrite the reciprocal as a negative power.Apply the power rule.
Question 2

Differentiate with respect to . Work on .

Check answer
Rewrite the reciprocal as a negative power.Apply the power rule.
Question 3

Differentiate with respect to . Work on .

Check answer
Rewrite the reciprocal as a negative power.Apply the power rule.
Question 4

Differentiate with respect to . Work on .

Check answer
Rewrite the reciprocal as a negative power.Apply the power rule.
Question 5

Differentiate with respect to . Work on .

Check answer
Rewrite the reciprocal as a negative power.Apply the power rule.
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