Find derivative of simple polynomial (integer powers)

Differentiate polynomial expressions involving only integer powers, including negative integer powers, without requiring algebraic rearrangement beforehand.

29 questions · Easy -1.3

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OCR MEI C2 Q9
5 marks Moderate -0.8
A is the point \((2, 1)\) on the curve \(y = \frac{4}{x^2}\). B is the point on the same curve with \(x\)-coordinate \(2.1\).
  1. Calculate the gradient of the chord AB of the curve. Give your answer correct to 2 decimal places. [2]
  2. Give the \(x\)-coordinate of a point C on the curve for which the gradient of chord AC is a better approximation to the gradient of the curve at A. [1]
  3. Use calculus to find the gradient of the curve at A. [2]
AQA AS Paper 1 2024 June Q9
5 marks Moderate -0.8
A curve has equation \(y = f(x)\) where $$f(x) = x(6 - x)$$
  1. Find \(f'(x)\) [2 marks]
  2. The diagram below shows the graph of \(y = f(x)\) On the same diagram sketch the gradient function for this curve, stating the coordinates of any points where the gradient function cuts the axes. [3 marks] \includegraphics{figure_9}
AQA Paper 3 2018 June Q2
1 marks Easy -1.8
A curve has equation \(y = x^5 + 4x^3 + 7x + q\) where \(q\) is a positive constant. Find the gradient of the curve at the point where \(x = 0\) Circle your answer. [1 mark] \(0\) \quad \(4\) \quad \(7\) \quad \(q\)
Edexcel AS Paper 1 Specimen Q2
4 marks Easy -1.2
The curve \(C\) has equation $$y = 2x^2 - 12x + 16$$ Find the gradient of the curve at the point \(P (5, 6)\). (Solutions based entirely on graphical or numerical methods are not acceptable.) [4]