SPS SPS SM Pure 2023 October — Question 1

Exam BoardSPS
ModuleSPS SM Pure (SPS SM Pure)
Year2023
SessionOctober
TopicProduct & Quotient Rules

  1. technology.
    1. Differentiate with respect to \(x\)
      1. \(x ^ { 2 } \mathrm { e } ^ { 3 x + 2 }\),
      2. \(\frac { \cos \left( 2 x ^ { 3 } \right) } { 3 x }\).
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    (i) The curve \(C\) has equation $$y = \frac { x } { 9 + x ^ { 2 } }$$ Use calculus to find the coordinates of the turning points of \(C\).
    (ii) Given that $$y = \left( 1 + \mathrm { e } ^ { 2 x } \right) ^ { \frac { 3 } { 2 } }$$ find the value of \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) at \(x = \frac { 1 } { 2 } \ln 3\).
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