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Original practice · Free Online RevisionSkill · first principles
Using first principles, find the derivative of f(x)=x².
CalculusAdvancedMaths revision
Differentiation
Understand derivative as local rate of change and apply core differentiation rules accurately.
Focus points
✓Connect derivatives to limits and gradients.
✓Use product, quotient and chain rules.
✓Interpret derivatives in context.
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Practice setQuestion lineup
Try each question first, reveal a hint when you need one, then check the worked answer. Mark them done as you go — finish the set to claim your chips.
10 revision questions
Question 2FluencyCore
Original practice · Free Online RevisionSkill · power rule
Differentiate y=5x⁴−3x²+7x−1.
Question 3FluencyCore
Original practice · Free Online RevisionSkill · chain rule
Differentiate y=(3x−2)⁵.
Question 4FluencyCore
Original practice · Free Online RevisionSkill · product rule
Differentiate y=x²eˣ.
Question 5FluencyCore
Original practice · Free Online RevisionSkill · quotient rule
Differentiate y=(x²+1)/(x−1).
Question 6ApplicationCore
Original practice · Free Online RevisionSkill · stationary points
For f(x)=x³−6x²+9x, find stationary points.
Question 7ApplicationCore
Original practice · Free Online RevisionSkill · rates of change
A particle has displacement s(t)=t³−6t²+9t. Find velocity at t=2 and acceleration at t=2.
Question 8ChallengeStretch
Original practice · Free Online RevisionSkill · logarithmic differentiation
If y=xˣ for x>0, find dy/dx using logarithmic differentiation.
Question 9ChallengeStretch
Original practice · Free Online RevisionSkill · implicit differentiation
Differentiate implicitly x²+y²=25 and find dy/dx at (3,4).
Question 10ReasoningStretch
Original practice · Free Online RevisionSkill · derivative reasoning
Explain geometrically why f′(a)=0 is necessary but not sufficient for a local extremum.