Chain rule with single composition

Questions asking to differentiate composite functions of the form f(g(x)) where the chain rule is required, such as (ax+b)^n, √(ax²+b), or similar single-layer compositions.

7 questions · Moderate -0.8

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OCR MEI C3 2008 January Q1
4 marks Moderate -0.8
1 Differentiate \(\sqrt [ 3 ] { 1 + 6 x ^ { 2 } }\).
OCR MEI C3 Q2
3 marks Moderate -0.8
2 Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) when \(y = \sqrt { 1 + x ^ { 3 } }\).
OCR MEI C3 Q3
6 marks Moderate -0.8
3 Differentiate the following functions.
  1. \(\quad y = \left( x ^ { 2 } + 3 \right) ^ { 5 }\)
  2. \(y = \frac { \sin 2 x } { x }\)
OCR MEI C3 Q6
4 marks Moderate -0.8
6 Given that \(y = \sqrt [ 3 ] { 1 + x ^ { 2 } }\), find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\).
OCR MEI C3 Q2
4 marks Moderate -0.8
2 Differentiate \(\sqrt [ 3 ] { 1 + 6 x ^ { 2 } }\).
OCR MEI C3 2011 January Q1
4 marks Moderate -0.8
1 Given that \(y = \sqrt [ 3 ] { 1 + x ^ { 2 } }\), find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\).
AQA Paper 1 2024 June Q6
2 marks Moderate -0.8
6 Use the chain rule to find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) when \(y = \left( x ^ { 3 } + 5 x \right) ^ { 7 }\)