Differentiation of logarithmic functions

Questions requiring differentiation of ln(f(x)) or more complex logarithmic expressions using the chain rule.

2 questions · Moderate -0.8

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Edexcel C3 2011 June Q1
5 marks Moderate -0.8
Differentiate with respect to \(x\)
  1. \(\quad \ln \left( x ^ { 2 } + 3 x + 5 \right)\)
  2. \(\frac { \cos x } { x ^ { 2 } }\)
SPS SPS SM Pure 2020 October Q2
5 marks Moderate -0.8
  1. Find \(\frac{dy}{dx}\) if \(y = 4\ln(3x)\) [2]
  2. Differentiate \(\frac{2x}{\sqrt{3x+1}}\) giving your answer in the form \(\frac{3x+c}{\sqrt{(3x+1)^p}}\), where \(c, p \in \mathbb{N}\) [3]