Basic power rule differentiation

Questions asking to differentiate simple polynomials and power functions (including negative and fractional powers) without composition, using only the power rule.

19 questions · Easy -1.4

Sort by: Default | Easiest first | Hardest first
CAIE P1 2003 June Q3
5 marks Easy -1.3
3
  1. Differentiate \(4 x + \frac { 6 } { x ^ { 2 } }\) with respect to \(x\).
  2. Find \(\int \left( 4 x + \frac { 6 } { x ^ { 2 } } \right) \mathrm { d } x\).
Edexcel P1 2018 Specimen Q1
6 marks Easy -1.3
  1. Given that \(y = 4 x ^ { 3 } - \frac { 5 } { x ^ { 2 } } , x \neq 0\), find in their simplest form
    1. \(\frac { \mathrm { d } y } { \mathrm {~d} x }\),
    2. \(\int y \mathrm {~d} x\)
      a) \(y = 4 x ^ { 3 } - 5 x ^ { - 2 }\)
      \(\frac { d y } { d x } = 12 x ^ { 2 } + 10 x ^ { - 3 }\)
      b) \(\int 4 x ^ { 3 } - 5 x ^ { - 2 } d x\)
      \(= \frac { 4 x ^ { 4 } } { 4 } - \frac { 5 x ^ { - 1 } } { - 1 } + c = x ^ { 4 } + 5 x ^ { - 1 } + c\)
Edexcel C12 2018 October Q3
7 marks Easy -1.2
3. Given that \(y = 2 x ^ { 3 } - \frac { 5 } { 3 x ^ { 2 } } + 7 , x \neq 0\), find in its simplest form
  1. \(\frac { \mathrm { d } y } { \mathrm {~d} x }\),
  2. \(\int y \mathrm {~d} x\).
    VIIN SIHI NI IIIIM ION OCVIIN SIHI NI JYHM IONOOVI4V SIHI NI JIIIM ION OC
Edexcel C1 2005 June Q2
5 marks Easy -1.2
Given that \(y = 6 x - \frac { 4 } { x ^ { 2 } } , x \neq 0\),
  1. find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\),
  2. find \(\int y \mathrm {~d} x\).
OCR MEI C2 2005 June Q1
4 marks Easy -1.2
1 Differentiate \(x + \sqrt { x ^ { 3 } }\).
OCR MEI C2 Q4
5 marks Easy -1.8
4 Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) when
  1. \(y = 2 x ^ { - 5 }\),
  2. \(y = \sqrt [ 3 ] { x }\).
OCR MEI C2 Q7
3 marks Easy -1.2
7 Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) when \(y = \sqrt { x } + \frac { 3 } { x }\).
OCR MEI C2 Q1
4 marks Easy -1.2
1 Differentiate \(x + \sqrt { x ^ { 3 } }\).
OCR MEI C2 Q8
5 marks Easy -1.8
8
  1. Differentiate \(12 \sqrt [ 3 ] { x }\).
  2. Integrate \(\frac { 6 } { x ^ { 3 } }\).
OCR MEI C2 2012 June Q1
3 marks Easy -1.2
1 Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) when \(y = \sqrt { x } + \frac { 3 } { x }\).
OCR MEI C2 2013 June Q1
5 marks Easy -1.8
1 Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) when
  1. \(y = 2 x ^ { - 5 }\),
  2. \(y = \sqrt [ 3 ] { x }\).
OCR MEI C2 2015 June Q1
5 marks Easy -1.8
1
  1. Differentiate \(12 \sqrt [ 3 ] { x }\).
  2. Integrate \(\frac { 6 } { x ^ { 3 } }\).
OCR MEI C2 2016 June Q1
5 marks Easy -1.8
1
  1. Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) when \(y = 6 \sqrt { x }\).
  2. Find \(\int \frac { 12 } { x ^ { 2 } } \mathrm {~d} x\).
OCR PURE 2020 October Q1
6 marks Easy -1.2
1
  1. Find \(\frac { \mathrm { d } } { \mathrm { d } x } \left( x ^ { 3 } - 3 x + \frac { 5 } { x ^ { 2 } } \right)\).
  2. Find \(\int \left( 6 x ^ { 2 } - \frac { 2 } { x ^ { 3 } } \right) \mathrm { d } x\).
Edexcel C1 Q3
5 marks Easy -1.3
3. $$y = 7 + 10 x ^ { \frac { 3 } { 2 } } .$$
  1. Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\).
  2. Find \(\int y \mathrm {~d} x\).
Edexcel C1 Q5
7 marks Easy -1.2
5. Given that $$y = x + 5 + \frac { 3 } { \sqrt { x } }$$
  1. find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\),
  2. find \(\int y \mathrm {~d} x\).
Edexcel C2 Q2
10 marks Moderate -0.8
2. (i) Differentiate with respect to \(x\) $$2 x ^ { 3 } + \sqrt { } x + \frac { x ^ { 2 } + 2 x } { x ^ { 2 } }$$ (ii) Evaluate $$\int _ { 1 } ^ { 4 } \left( \frac { x } { 2 } + \frac { 1 } { x ^ { 2 } } \right) \mathrm { d } x$$
AQA AS Paper 1 2023 June Q5
7 marks Easy -1.2
5 (b) & 5 (a) Given that \(y = x \sqrt { x }\), find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\)
\hline \end{tabular} \end{center}
AQA Paper 1 Specimen Q2
1 marks Easy -1.8
2 A curve has equation \(y = \frac { 2 } { \sqrt { x } }\)
Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\)
Circle your answer.
[0pt] [1 mark] $$\frac { \sqrt { x } } { 3 } \quad \frac { 1 } { x \sqrt { x } } \quad - \frac { 1 } { x \sqrt { x } } \quad - \frac { 1 } { 2 x \sqrt { x } }$$