Grade 12 Maths · Calculus

Differentiate using the power rule

Find the derivative of each term by bringing the power down and lowering it by one (for example the derivative of 3x⁴ is 12x³).

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First Derivative Calculus Grade 12 | PolynomialsKevinmathscience

First Derivative Calculus Grade 12 | RootsKevinmathscience

The Power Rule For DerivativesThe Organic Chemistry Tutor

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Question 10.2 · November 2024 · Paper 1 · National (DBE) · 5 marks

A cyclist rode from town P and stopped at town T. The speed (in km/h) at which this cyclist rode, is represented by the equation

s^{'} (t) = - 3 t^{2} + 18 t

. NOTE: Speed is the rate of change in distance with respect to time.

10.2 Calculate the distance between town P and town T.(5)

Work it out on paper first. Then mark yourself with the official memo, one tick at a time.

More past paper questions: differentiate using the power rule

Work each one out first, then open the memo and check every tick.

3. Question 8.2.1 · May/June 2025 · Paper 1 · National (DBE) · 2 marks
8.2 Determine:
8.2.1 $\frac{d}{d x} [3 x^{2} - 4 x]$ (2)
Show the memo (2 ticks)Memo
1. ✓
  Differentiate the first term $\frac{d}{d x} [3 x^{2}] = 6 x$
  1 mark · Differentiate using the power rule
2. ✓
  Differentiate the second term $\frac{d}{d x} [- 4 x] = - 4$
  $∴ \frac{d}{d x} [3 x^{2} - 4 x] = 6 x - 4$
  1 mark · Differentiate using the power rule
4. Question 8.1.1 · November 2024 · Paper 1 · National (DBE) · 2 marks
8.1 Determine:
8.1.1 $\frac{d}{d x} [3 x - 5 x^{2}]$ (2)
Show the memo (1 tick)Memo
1. ✓
  Apply power rule $3 - 10 x$
  2 marks · Differentiate using the power rule
5. Question 8.2.1 · May/June 2024 · Paper 1 · National (DBE) · 3 marks
8.2 Determine:
8.2.1 $\frac{d}{d x} (4 x^{6} + 2 x^{2})$ (3)
Show the memo (3 ticks)Memo
1. ✓
  Simplify first term to power form $2 x^{3}$
  1 mark · Simplify and combine surds
2. ✓
  Derive first term $6 x^{2}$
  1 mark · Differentiate using the power rule
3. ✓
  Derive second term $22 x$
  1 mark · Differentiate using the power rule
6. Question 9.2 · September 2024 · Paper 1 · Provincial · 2 marks
9.2 Given: $h (x) = 4 x^{3} + 5 x$ . Substantiate whether it is possible to draw a tangent to the graph of h that has a negative gradient.(2)
Show the memo (2 ticks)Memo
1. ✓
  Derivative $h^{'} (x) = 12 x^{2} + 5$
  1 mark · Differentiate using the power rule
2. ✓
  ExplanationAlways positive
  1 mark · Find equation of a tangent

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